Hello guys, so today we are going to start our another chapter which is again very crucial chapter This is linear equations in two variables So I just waiting for a couple of more minutes to For people to join in and then we'll start. Okay, so let's start. Okay, so we are going to discuss in this Session Linear equations so the agenda is to discuss linear equations and you know linear equations especially in two variables and after that what we'll try to do is we'll also see How to solve linear equations Solving linear equations, then we also talk about consistency consistency of solutions or Right, and then towards the end. We'll also see what problems and for autonomous syllabus Specifics will discuss towards the end Okay, so let us start so basically, you know the definition will quickly run through the definitions and all the basic Concepts and then we'll try to solve as many problems as as possible So a pair of linear equations in two variables x and y can be represented as a brightly as follows a1 x plus b1 y plus c1 equals to 0 and a2 x plus b2 y plus c2 equals to 0 Where a1 a2 b1 b2 and c1 c2 are real numbers such that Yeah You have to you have to see that a1 a1 and e2 both together cannot be 0 so a1 is not equal to 0 so basically do both together cannot be 0 a1 and and b1 Not equal to 0 Simultaneously cannot be possible right so hence all of them together cannot be zero hence this this particular this particular expression has been given Okay, so this is my definition of linear equations now next is graphically or geometrical a pair of linear equation in two variables represent a pair of straight lines Okay, so we know and let me Just draw a graph so hence how does linear equation? Look like in a graph, okay, so let's say this is x this is why Okay, so linear equation will be of this form where this is a1 x plus b1 y plus c1 equals to 0. This is not equal to this is plus here Okay, so a2 x plus b2 y plus c2 equals to 0. So another equation could be something like this so Right, so this this one is let's say this one is a2 x plus b2 y plus c2 equals to 0 Okay, and this point of intersection. This is the point of intersection Okay, this point here is the point of intersection, right? So hence we say that These two lines are intersecting.  That means coefficient of x in the first equation divided by coefficient of x in the second equation must not be equal to coefficient of y in the in the in the first equation and Sorry, this is not here. So this is b1 by b2. So this is the condition for a Unique solution or one solution one pair of solution that is pair of solution means what you will get x and y One one set of x and y you will get right if they are parallel The other condition could be if they are parallel. Let's say Let's say this is parallel. Okay, so parallel lines So this is x this is y and again if this is equation number one Let's say this is a1 x plus b2 y plus c sorry b2 b1 y plus c1 equals to 0 and this line is a2 x plus b2 y Parallel by a2 Is equal to b1 by b2 Sorry for parallel line this must not be equal So a1 by a2 is equal to b1 by b2 is not equal to c1 by c2 Okay, so this is for parallel lines and for a coincidence. This is case number one This is case number two and case number three is this coincidence. So coincidence is this that means all the ratio All the ratio must be equal. So for coincidence or overlapping coincident lines Coincident lines or coincidence coincident lines the ratio should be all equal a1 by a2 is equal to b1 by b2 Is equal to c1 by c2 Right, this is our linear equation You know consistency criteria Okay, so Okay, now so a pair of linear equations in two variables can be solved by two methods What are two methods graphical method one is graphical method Another is algebraic method, right and in algebraic method. You also know there are three processes one is called substitution Then there is something called elimination And third is cross multiplication Right, so we'll see all these methods one by one, right? And uh, please be very very careful in linear equations If the question categorically asks you to use one particular method Then do not solve the question using some other method So hence read the question carefully Many times they would mention which particular method they are asking for You can use your other methods to check whether the solution which you have arrived at is correct or not Okay, so to solve a Pair of linear equation in two variables by graphical method We first draw the lines represented by them If the pair of lines intersect at a point then we say that the pair is consistent And the coordinates of the point Is the unique solution is the unique solution Now if the pair of lines are parallel then the pair has no solution and is called inconsistent pair of equation It's called inconsistent. So be Careful about these keywords. They will be used. They will be they will be using so consistent Then inconsistent and then if the pair of coincident lines, then it has infinitely many solutions So there are three things each point on the line being one solution In this case, we say that the pair of linear equations is consistent with infinitely many solutions. So, yes What all one is you have unique pair solution or unique solution This is then there are infinitely many solution Infinitely many and then third is no solution in these cases is called consistent the system is consistent consistent Consistent And in this case it is called inconsistent Okay, so you must remember these because in very last year also in 2018 there has been one question Where they had asked a question on consistency of the two equations So let's start Yeah, so You know, this is the algebraically. Let's see and understand how to solve. Let's say in this case if two equations are given So, let us say a x a 1 x plus b 1 y plus c 1 equals to 0 is given And then a 2 x plus b 2 y plus c 2 is equal to 0 given excuse me So, let us say let us see through Algebra geojibra Okay, so here is the Two equations. So let's say y equals to 3 x plus 2 here And y is equal to 2 x minus 5 these two equations are given. So what you need to do is You need to First of all plot the graph of first equation then plot the graph of second equation And wherever they are intersecting for example, this is the point here. So if you see This point this point is the point of intersection a minus 7 minus 19 is the solution to this pair of System of equations. So how do you plot? I will just briefly give you a Briefly give you a process. So let's say you had 2 x plus 3 y plus 1 equals 0 and you had 3 x minus 2 y plus 2 equals 0 then you convert or let's say transform them in such a way that it is in y equals to mx plus c form So, how do I write this? I can write this as 3 y equals negative 2 x negative 1 And y hence is equal to minus 2 upon 3 x minus 1 upon 3 correct Then what you need to do is you need to just simply need to you know Put random values of x usually we start from 0 1 2 and all that and some negative 1 and negative 2 and all that And then plot at least 2.2 points are good enough to plot a linear equation. So So let's say if you you know get 2 points 2 points x and y So let's say if you put x equals to 0 here, what will you get? You will get y equals negative 1 by 3 so put that so hence first ordered pair is 0 and minus 1 by 3 Okay Right and simply if you put x equals to 1 then y so when x equals to 1 then y is equal to minus 2 by 3 minus 1 by 3 is minus 1 Okay, so another point is 1 comma minus 1. So what next you need to simply need to plot x and y in a graph paper They will give you a graph paper and then what do you need to do plot 0 comma 1 point minus 1.3 I'm not doing it with scale you guys when you do it you have to do it using scale and graph paper So 0 comma minus 1 by 3 will be this is x equals to 0 and this is let's say minus 1 by 3 Okay, so 0 comma this is x equals to 0 and y minus 1 by 3 and The second point 1 comma minus 1 will be 1 and maybe this is minus 1 Let's say this is 1 and this is minus 1 to this point. So hence you have to draw it freehand And using a scale you should do so you will get this line Similarly in this case you will get You know positive slope value. So hence it is nothing but y equals here I'm writing in one step itself. So this is 3 by 2 x plus 1 Okay, so this line is somewhere like that Okay, so this is so hence You know this line and this was the line initially. So hence, whatever is the This is the point. So hence you have to draw perpendicular from here perpendicular from here. So basically you have to If you see this perpendicular has to be dropped from here. So this is x And this is y Right, so hence, whatever is the x and y coordinate here you'll have to Write that as a solution. So this is a graphical solution. Okay Fair enough Now let's go to the algebraic form. So there are three substitution elimination and cross multiplication method And I think we should be taking examples to Explain these in detail. So just let me take an example so that we can solve One one question so that all the three methods are All the three minutes are covered Okay, so let me take a question 2x minus y minus 3 so the question is So let us go down to our gap. So let me just explain it here Okay, so we are going to Take one question to explain All the three methods. So let's say we have to solve the question is solve Solve this pair what pair 2x minus y 2x minus y minus 3 equals 0 and 4x plus y minus 3 equals 0 So 2x minus y minus 3 equals 2 0 4x plus y minus 3 equals 2 0 and we'll see each method one by one Now clearly this is of the form of a 1x plus b 1 y plus c 1 equals 0 And the second one is a 2x plus b 2 y plus c 2 equals 0 And clearly a 1 is equal to 2 b 1 is equal to negative 1 and c 1 equals negative 3 Then a 2 equals 4 here b 1 and c 2 equals negative 3 again right now Let's us first take a substitution What is substitution? You have to first express one of the variables in the Form of other variables and you can use any one any one of the variables But but usually we try to avoid fractions So hence instead of expressing x in the form of y I would have gone for expressing y in terms of x because that would have eliminated any Appearance of fractions in the equation. So if you see It's always a good practice to keep numbering the equations and then mention the equation in terms of numbers So you can say from 1 from equation 1 you can say y equals Be very very careful with sign guys. So if you're writing y that means y is going to the right hand side here So y is equal to 2x minus 3 It's always a good practice to go a little slow here Uh, because if you miss any sign then the entire set entire equation is Going to be wrong. So hence y equals 2x minus 3 And now this is 3 This is equation number 3. So you'll write Using using 2 and 3 using 2 and 3 Okay using 2 and 3 what can you say you can say put y back into the second equation So 4x plus y now I can substitute y for this thing which we just found out So let us say let us say 2x minus 3 here minus 3 here equals to 0 and then it is 6x Minus 6 equals to 0 which becomes 6x equals to 6. So hence x equals 1 Right x equals to 1. So if x equals to 1 then clearly what is y? y I will use equation 3. So from 3 from 3 y equals 2 times 1 minus 3 Which is nothing but negative 1 Correct, let's check them. Let's check it whether it is correct or not. So equation was 2x minus y minus 3 equals 0 So if you put x equals to 1 You will get 2 here and then y is equal to minus 1. So minus minus 1 is plus 1 So this is 3 minus 3 which is 0 So hence this particular equation and second equation is also satisfied if we check 4 into 1 minus 1 minus 3 equals to 0 So both x equals to x equals to 1 And y is equal to minus 1 is the correct solution So we just check this is called substitution. What did we do? We express one of the variables in terms of the other and then Okay, so you use one in terms of the other and then Then substitute in the second equation and then Find the other variable. Okay Second is elimination How do you use elimination same set of equations? I'll use the question is 2x minus y minus 3 equals 0 And second one is 4x Plus y minus 3 equals to 0 This is equation number 1. This is equation number 2. So what do we do? We need to Eliminate so elimination as the name suggests you'll have to eliminate one of the variables Either you can eliminate x or you can eliminate y and how do you eliminate? We manipulate the coefficients of x and y so that the coefficient of x or y becomes same or with opposite sign Right and then either depending upon the sign of the Proficient will add or subtract. So I'll do both case in this case. So let us say I want to eliminate y so if you see if you simply add the two equation Adding two equation means add lhs to lhs add rhs to rhs. So if you simply add all of them So 2x plus 4x will give c 6x Minus y plus y will give you 0 And minus 3 minus 3 is minus 6 equals 0. So Very simply x comes out to be my 6 upon 6 which is 1 Okay Now what you can do is you can deploy x back into the any of any of these equations and find the value of 1 So for example, if I put x putting x equals to 1 Putting x equals to 1 in let's say 1 So it will become 2 into 1 minus y minus 3 equals 0 So ends y is clearly 1 see if you see this is matching with our previous solution Whatever we found out here if you see x equals to 1 and yeah So this is the solution we obtained in the previous case through substitution The same thing we are getting through elimination as well Right another way of let's say in this case we use substitution also But we can use direct elimination here also how so let us say I have to eliminate x So I have to eliminate x. So what I'll do is I'll multiply the first equation So let me write it once again. So 2x minus y minus 3 equals 0 And 4x plus y minus 3 equals 0 now I'm saying I have to eliminate x So how do you eliminate x first try to you know match the coefficient? Okay, match the coefficient. So if you see coefficient of x here is 2 and here is 4 So if I multiply this equation by 2 they will match Okay, so after so 2 into 1 will give me what? 4x minus 2 y minus 6 equals 0 Let us say this is equation number 3 And you write second equation once again 4x plus y minus 3 equals 0. So this is equation number 2 Now what you do you subtract the second equation from the first one. So hence this will become Negative this will become negative this will become positive and hence if you add now you will get 0 minus 3 y Is minus 3 equals 0. So from here y equals to negative 1 Yeah And again you put back y equals to minus 1 in any of the equations. Let's say putting y equals to putting putting y equals negative 1 In let's say equation number In equation number 1 What will you get 2x minus minus 1 minus 3 equals 0 So which is nothing but 2x minus 2 equals 0. So x equals 1. So this is the solution. So we saw both the Both the ways right. So what all did we see so far? We saw first is substitution. You know what to do Again, I'm telling you please be very careful if they have mentioned any particular method do not use any other method second is Elimination these two we learned and the third one which we are going to learn is the cross multiplication Yeah, so the third one is Third one is cross multiplication Now in cross multiplication, there are few things to be taken care of Yeah, in which form you are writing the equation is also important because If you miss the you know one particular form has one particular format of form as in, you know The pattern in which you have to remember the formula Okay So I prefer that Formulate where all the All the terms are on one side Okay, what do I mean?  So the two equations are again if you see 2x minus y minus 3 equals 2 0. So this is one is One is 2 2x minus y minus 3 equals 0 and the other one was 4x plus y minus 3 equals 2 0 now here if you see There is nothing on the right hand side only 0 right another way of writing this could be 2x minus y equals 3 and 4x plus y equals 3 so make sure That you follow one because if you have this particular format ready Then you have another Yeah, just a minute guys There's some issue yes, so Yeah, so what I was saying is you have to have one particular format Yeah, so let's say if you are if you're using this format this left hand side Okay, then you have to have one one type of formula if you are having this particular type Format then another type of formula. So hence I generally use this one And hence in this case what will be the formula to be used so I write it like this So make sure that all of them are In the same side and only zero is there on the Okay, so hence the formula goes like this x upon You have to write b1 b2 and then you have to write c1 c2 And then this equals to y upon c1 c2 and then a1 a2 and this is equal to 1 upon a1 a2 and then b1 b2 And then you have to multiply top left to bottom right first top left bottom right always Top left bottom right always first Okay, and then you can write this as x upon Top left bottom right right so it will go in this direction top left to bottom right you have to multiply So you will get b1 c2 minus b2 c1 And this is equal to y again same thing top left bottom right so c1 a2 minus c2 a1 And this is equal to 1 upon a1 b2 minus a2 b1 Okay, so hence here what will happen this implies x will be equal to simply If you equate this part with this part All three are equal so I can say x equals to b1 c2 minus b2 c1 divided by a1 b2 minus a2 b1 And similarly y is equal to y is equal to you have to now equate these two this this to this Right, so hence you will get y is equal to c1 a2 minus c2 a1 upon a1 b2 minus a2 b1 Right, so let us deploy the formula and see whether we are getting the correct answer or not So let us say what was p1 and all that so let us Let us first find out a1 b1 and all that okay. Let us read it again So the two equations were the two equations were this So clearly our a1 is equal to two And b1 equals to minus one and c1 equals to negative three a2 similarly equals to four b2 is equal to one and c2 equals to negative three Right, so let us deploy these values here x x equals to now v1 c2 so negative one into c2 Which is negative three then minus b2 which is one into c1 which is negative three divided by a1 b2 so two into one so two into one Minus a2 b1 so a2 is four into b1 is negative one So hence if you see this is nothing but three plus three divided by two minus Two plus four which is nothing but one And in this case c1 c1 c1 a2 so c1 is negative three and a2 was four so this into four minus c2 is negative three into a1 which is two divided by same thing two into one minus four into negative one And if you see this comes out to be minus 12 Plus six divided by six which is nothing but negative one So if you see in all the three cases we got the right answer Is it x equals to one and y equals to negative one in all the three cases what case is in substitution in elimination and third is cross multiplication Okay, so now we will come back to our This thing solution of the other solutions, sorry the other important topics So again, we are coming back to the consistent consistency part of it So if you see there are two equations a1 x and Plus b1 y plus c1 equals to zero And a2 x plus b2 y plus c2 equals to zero our standard form And then we say that if a1 by a2 is not equal to b1 by b2 Then the pair of linear equation is consistent. Please remember Inequality of the first ratio first two ratio is consistency. That means that you will get one pair of solution here Here in in the second case a pair of linear equation is inconsistent when a1 by a2 is equal to b1 by b2 But it is not equal to c1 by c2. Okay next and the third is a1 by a2 a1 by a2 is equal to b1 by b2 is equal to c1 by c2 in this case These are these lines are parallel lines. So you can remember like that So Chris cross that is intersecting line means not equal to write and then parallel line is the third the second and the third ratios should not be equal and coincident line are When all the ratios are equal Okay, so we'll be seeing this these applications a little later. Yeah Now here is the question now. Now. Let us start solving questions So the question is represent the following pair of equations graphically and write the coordinates of points Where the lines intersect y axis? Okay, so we will use the software here Usually you need you know, you know how to do it if you have a graph paper So let me just take this graph paper. Okay So let us say this is like a graph paper field now. Let us first write down the two to x plus 3 y is equal to 6 and 2 x minus 3 y is equal to 12 x plus 3 y is equal to 6. So hence I have x plus and the other one is 2 x minus 3 y equals to 12 So this is 2 x These are the two equations I have to solve graphically. So if you see there is a kind of graph paper already here So we'll use that and that's how you have to do there Also, I'm not using a scale because I'm using a tab. So let us say, uh, first of all We draw a graph paper or let's say x and y Right, so my drawing will be a little rough. So this is x This is y. Okay, and this is negative x You don't do full negative x and negative y as much as The question demands now. What is it? So x plus 3 y is equal to 6 So x plus 3 y is equal to 6. This is the first right, so hence Let us first Let us first plot the first equation. So hence if you see the first equation is x is equal to 6 minus 3 y This is one. So let us plot or let us find out the values of x and y 6 minus 3 y right now. So hence let's say let us say this is x and this is y. So when y equals to 0 You should take one of them as 0 then it becomes easier to find out when y equals to 0 x equals to 6 And when x equals to 0 You will see if you put x equals to 0 you will get y is equal to 2 Right, so when y is equal to 0 x equals to 6 And when x equals to 0 y is equal to 6 by 3 that is 2. So now you can easily plot this So first point is 6 comma 0. So 1 2 3 4 5 6. This is 6 Comma 0. So let me use this color. So this is my first point 6 comma 0 you write it 6 comma 0 and then 0 comma 2 will be somewhere here 0 comma Okay, then what you need to do Right, so hence what you need to do is you need to just free with a scale We join these So this is the first equation now second equation Second equation is 2 x minus 3 y equals to 12. So yes, again you can write From here I am writing now here. So it can be written as x equals 12 plus 3 y 12 plus 3 y by 2 12 plus 3 y by 2 So which is nothing but 6 plus y by 2 No, 6 plus sorry 6 plus 3 y by 2. So hence again you can plot this we'll say x and y So when y is 0 When y is 0 x is again 6 And y is 0 x is again 6 And when x is 0. So y will be nothing but negative 12 by 3 So here you can you can say when when x equals to 0 When x equals to 0 y will be negative 4 Let us plot it. So 6 comma 0 is the same point and 0 comma minus 4 So this is 0 comma 1 1 2 3 4 so this is And hence the line is something like that So clearly the point of intersection is 6 comma 0 because 6 comma 0 satisfies 4 Let's check whether it is actually true. So if you put 6 comma 0 here It is satisfying the first one and if you put 6 comma 0 2 into Yeah, second or it is satisfying. So then 6 comma 0 is Okay, so this is how graphically you have to solve this Now now comes this kind of how we are solving Linear equations now if you see this is not a linear equation here This is not a linear equation not a linear equation Why because the power of x is negative 1 and power of y is also negative 1 both of them But it can easily be transformed into linear equation how by Assuming or substitution let us say we will say let us say u is equal to 1 upon sorry Yeah, 1 upon x and v is equal to 1 upon y Now the moment you say that the equations are transformed as 2 u plus 2 by 3 v equals 1 by 6 So simply multiply the entire equation by 6 simplify it you will get 12 u plus 4 v is equal to 1 so this can be equation number 1 Secondly in the second equation you will get 3 u plus 2 v equals 0 3 u plus 2 v equals 0 and then this is equation number 2 Now what can you do you can eliminate now let us multiply this equation by 4 So you can 12 u plus 8 v is equal to 0. This is equation number 3 Now what do you do is 1 or Yeah, so you can do 1 minus 3 If you do that You will be eliminated and 4 v minus 8 v is negative 4 v Is equal to 1 minus 0 which is 1 so v is equal to negative 1 upon 4 Okay, and then Another if you put v equal to this thing will get v equal to minus 1 by 4 if you put you will get u But the other way could be you multiply the Um the second one The second one the second equation equation number 2.  This is equation number 4 Right now what you can do is 2 1 minus 4 So this will give you the view minus 6 u is 6 u And 4 v and 4 v gets eliminated and then you will get 1 minus 0 as 1. So u is equal to 1 upon 6 Right. So when v is equal to 1 minus 1 by 4 you can write. What was v? v was 1 upon y So y is equal to 1 upon v, which is nothing but negative 4 You can say x equals to 6 You were one upon x so x equals to 6. Let's check whether this is correct or not So first one equation number 1 would be nothing but 2 upon 6 on the LHS Plus 2 by 3 into negative 4 Which is equal to 2 upon 6 and then this will be Uh Yeah, this is not this is somewhere. We made a mistake v equals to y equals to negative 4 2 upon x So we did some mistake somewhere. Maybe hence it is not coming 2 upon x So 2 upon 6 is 1 by 3 and then So it is correct. Correct. No worries. So 2 upon 6 is this is 2 upon 6 and this is nothing but negative 2 upon 12 So which is nothing but nothing but 4 minus 2 by 12. Am I right? 4 minus 2 Ah, so this will be 2 by 12 2 by 12 So I'm doing once again. Sorry for this confusion. So it is nothing but 4 minus 2 by 12 which is 2 by 12 Which is equal to 1 by 6. So which is correct Okay, so the moment you get x So this is this is correct. You can check the second equation also. So I am writing here second equation is 3 upon 6 Minus 2 upon 4 which is nothing but 0 points Solution is correct. So y is equal to minus 4 is correct and x equals to 6 is correct Okay, so this was the first question Let's go to by the way. This was a board paper question Again similar looking question. So here only you need to substitute one y is already formed if you see Here 4 x has to be changed. So then you can assume u to be equal to 1 upon x and then rewrite the equation So it will be 4 u plus 5 y equals 7 And 3 u plus 4 y equals 5 And then again do the repeat of the process you already know You multiply now. How do you so I will go for elimination again substitution would be the last thing I would do So what I'll do is I'll multiply 1 by multiply 1 this entire 1 by 3 and the and the Second equation number 2 by 4 y then my coefficient of u will be same So let us see. So this is 12 u Plus 15 y is it it 15 y equals 21 So multiply by 3 12 y 12 u plus 15 y plus 21 and then second is 12 u plus 16 y 12 u Plus 16 y is equal to 20. So this is equation number 3 And equation number 4 So 3 minus 4 3 minus 4 So what will happen 12 u 12 u? gets cancelled 15 y minus 16 y is negative y And this is equal to 21 minus 20 is 1. So y equals negative 1 Okay, so the moment you put y equals to 1 in any of these So let's say 4 u plus 5 into negative 1 is equal to 7 That means 4 u is equal to 7 minus minus 5 that is 12. So u is equal to 3 That means x equals 1 upon 3 Let's check Why because x equals to 1 upon u? Let's check equation number 1. We'll check 1 is 4 upon x. So 4 upon 1 by 3 Plus 5 y so 5 into negative 1 is equal to 12 minus 5 which is equal to 7 so satisfies an equation number 2 is 3 upon x That is 1 upon 3 plus 4 into negative 5 which is equal to 9 And i'm sorry y is minus 1. So this is minus 1 So hence it is 9 minus 4 which is 5. So this is also true Both are correct. So hence our solution was correct Okay next Okay, so Again the question happens is the moment you see Only variables. There's no numeral here. Then many people actually start panicking. You should not do that Yeah, so if you check there is no numeral here and many people are a worse of these kinds of questions But do not afraid. You know not panic not Do not You know get panicked with such with such questions And you know already how to solve but be very very careful while we are you are handling variables and don't mess up with the signs So let us see how do we do it and we know elimination is one of the uh, you know favorite mechanisms So we'll be using that method only So the equation number one. This is equation number one and equation number two. It always helps if you want you can Uh, simplify this.  Why am I doing this? Because if you do that then a and b gets eliminated In in both the terms in the first two terms, right? So you multiply ab Alternatively, you can take lcm of the first two terms denominator and then simplify and go ahead like that But here is how we will be doing it in this way So multiplying the entire equation by ab you will get b square x because a will get cancelled and it is a square y and this is equal to a q b plus a b q Okay, so hence, uh, you get this b square x plus a square y Is equal to a cube Okay, so so a q Uh, so b square x plus a square y equals a cube b Plus a b q and the second equation is x plus y is equal to ab So what I can do is I'll adopt elimination. So hence to equate the Proficient of x I will multiply with b square both the entire equation I will get b square x plus b square y is equal to a b q This is my equation number three and this is my equation number four So what I'm going to do is I will do three Minus four y because x will get eliminated simply so b square x minus b square x is zero And hence it will give you a square y minus b square y on the lhs And on the right hand side a b q and a b q gets eliminated you will get a q b okay So if you see what is it this what what is it now? So y is equal to y times a square minus b square is equal to a q b So y equals a q b by a q square minus b square right now to get To get y x do not substitute it rather again element you use elimination. So how will you eliminate? So now you multiply um The second equation by by a square right so you will do a square times x plus y equals a b So hence you will get a square x plus a square y is equal to a q b This is equation number five Okay, then how will you eliminate this? You will use three minus five So do three Minus five. So what will you get clearly a square y a square y is getting cancelled So hence you will get b square minus a square x Is equal to an a q b a q will go. So it is a b q So hence x equals nothing but a b q upon b square minus Okay So these are the two solution but other two solutions one is Y is equal to this so If you have time left towards the end of the paper Let's say once you are done with the paper your your time is left Then usually it is a good practice to put a star mark so that when you come back you please deploy these back into equations And c and especially if you see it is already satisfying the second equation. So most tend to give you the solution is correct The solution is Correct. So hence, but yes, nevertheless if you get time again check your calculations Next Second is now we see our question is on the consistency part, right? So determine the value of k these type of questions are there so that following linear equations have no solution So no solution means a one by a two is equal to b one by b two Should not be equal to c one by c two This is the criteria for no solution now So if you see you're the first What is a one here? Let us jot down A one is 3 k plus one right a two is equal to k square plus one right and b one Is equal to three b two is equal to k minus two c one is equal to negative two and c two is equal to negative five these are the Values just check once yes looks like it's correct Very good. So hence, what do we know? We know a one by a two so three k plus one by k square plus one a square plus one Is equal to three k plus uh b one by b two that means three upon k minus two And this must not be equal to minus two by negative five Right, right. So let us solve this part first So if you see cross multiply you'll get three k plus one into k minus two Is equal to three times k square plus one Which is equal to three k square minus six k plus k minus two Is equal to three k square plus three Okay, so three k square three k square gets cancelled So if you see minus five k Is equal to if you take it if you take a minus five k here and then minus two goes on to the Right hand side You will get Five right so k is equal to negative one Okay, k is equal to negative one is the solution Right, so if you put k equals to one negative one then anyways Yeah, so if you put k equals to one negative one then the system doesn't have any solution Okay next Now these are the word problems which are there So the first word problem is the sum of a two digit number and the numbers obtained number obtained by reversing the order Of its digit is 165 if the digit differs by three find the number. So let us say you will say what let us say the digits are x and y Okay Right, so the digits differ by three. So let us say Mod of x minus y will be equal to three Why am I using mod of x minus five because I don't know whether x is more or y is more Okay, so mod of x minus so hence you please keep in your mind that either x minus y is equal to three Or y minus x is equal to three both can be possible And now let us say if my if my number was x y x y then in in actuality the number is nothing but x y is just the position It's not a multiplication x y so the the number will be nothing but 10 x plus y and then they are saying Reverse this so the reverse number will be yx which will be nothing but 10 y plus x So if you add that both of them that is 11 x plus 11 y And the sum is they are saying the sum of two digit number and the number obtained by reversing the order is 165 So you will get x plus y is equal to 15 Correct x plus y is equal to 15 now x plus y is 15 and let us say x minus y was three So hence add both of them together you will get two x equals to 80 So x becomes six Correct, so hence the numbers are 96 and 36 if you add both of them So 96 and sorry not 36 69 96 and 69 so 96 plus 69 165 is the sum this is how you will solve this equation Okay Right, so what is the learning? Please remember number any two digit number is can be expressed as 10 x plus 10 x plus y right Next So a two digit number is such that the product of its digit is 20. So let us again start with x and y so let's say x and y are the digits So the product of its digit is 20. So x y is 20 If nine is added to the number The number would be nothing but what is the number 10 x plus y is the number Right if nine is added to it. So nine is added to this number The digits interchange their places that is this becomes 10 y plus x correct Why because if x y was the number not the product the position y is x y. So hence it is 10 x plus y And if it is y x then it is nothing but 10 y plus x That's what they're saying. So number plus nine The number the digits interchange their places. So 10 y plus x. So hence, what will you get? You will get Um nine x minus nine y plus nine is equal to zero Or y minus x equals to one if you see y minus x y minus x equals to one right this is one And the other equation is x y is equal to 20. So hence if you see this is our question which involves Not only lean soluble linear equation, but also quadratic equation. How let us see So hence I can say y is equal to x plus one from here And then use equation number one and equation number two To solve this so hence x times now y is x plus one And this is equal to 20 so it is x square Plus x minus 20 equals zero. So if you see this is we have got our quadratic equation So how to solve this split the middle term x square? It will be clearly five x minus four x minus 20 equals zero So hence if you see it is x times x plus five Minus four times x plus five equals zero So hence it becomes x plus five times x minus four equals zero and hence either x equals to minus five or x equals four But my dear friends x equals to minus five is not a feasible solution Not a feasible solution Or not a possible solution why because digits cannot be negative So what is the correct solution x equals to four? So if x equals to four, then you know y equals to five So let us check So x equals to four and hence y is equal to five because Four into five is 20 so hence the numbers are 45 and So hence if you add nine into it you'll get 54 the numbers the digits reverse you order Okay, so hence our solution is correct Okay, so numerator denominator type the sum of the numerator and the denominator of a fraction is 12 So let us say the let the fraction be So this is very typical Typical problem typical linear equation problem of cvc board So let the fraction be Let the fraction be x upon y Correct, and they're saying the sum of the numerator and denominator of a fraction is 12. That means x plus y equals 12. This is equation number one If the denominator is increased by three Denominator is increased by three. That means y becomes y plus three The fraction becomes one by two. So hence x upon y plus three equals One upon two so you have to find out x and y So let's cross multiply you'll get two x equals y plus three Right and hence you simplify it you will get two x minus y is equal to three. This is equation number two This is equation number two then what remains to do is add one and two One plus two. Why am I adding because if I can see there is a plus one as a coefficient of y negative one as a coefficient of y in the second equation Adding both you'll get three x And this is equal to 15. So x whatever five so x is Five when x is five Then you know y is seven Right. So if you see Five by seven plus three is actually one by two five by ten So hence our solution is correct Okay Great next Okay, now distance speed time type Abdul traveled 300 kilometers by train And 200 kilometers by taxi It took him five hours 30 minutes But if he travels 260 kilometer by train and 240 kilometer by taxi he takes six minutes longer Find the speed of the train and that of the taxi. So whatever is required you take assume that to be the variable So let's say speed of the train speed of the train be you Okay, and speed of speed of Taxi be V Okay speed of the train be you speed of the taxi be v now Abdul traveled 300 kilometers by train and 200 kilometers. So time taken right So time taken In case a so what is case a? Time taken is nothing, but you can write the formula first that is nothing but distance by If the velocity is constant, you can write distance by speed This is time taken. So hence let's first time taken first Let's take the first case right and then please also mention This is kilometers per hour right so that there is no confusion in units We look v kilometers per hour now time taken is distance upon speed So 300 kilometers by train that means time taken will be 300 upon u And then 200 by kilometer by taxi. So 200 upon v isn't it It took him five hours and 30 minutes that means it is 5.5 hours Right, but he travels 260 kilometers by train So 260 by u plus 240 by v Okay This will they are saying six minutes longer. So whatever the initial this thing was 5.5 but six minute is in minutes. So we'll have to convert it into hour, which is nothing but six upon 60 hours Please be very careful. So many people will just add six here and they will not be able to solve it. So be very very careful Now so how do we solve this so six by 60 is one upon 10 so point one This is nothing, but if you see this is nothing but 5.6 isn't it 5.6 now let us solve the um So hence if you see let us assume one by u is equal to x And one by v is equal to y. So the equations Which are left is nothing but 300 x plus 200 y equals 5.5 And 260 x plus 240 y is equal to 5.6 Okay, so now What you can do is you can simplify and then use substitution also So if you subtract these two equations together You will get very simple Relations to subtract these two so you'll get 40 x minus 40 y is equal to negative 0.1 Okay, so if you see this is nothing but x or you can you can write y minus x is equal to 0.1 by 40 I reverse the order of x and y So that I can eliminate negative sign from the right hand side, right? So hence you will get y minus x is equal to 1 by 400 Okay, now what you can do is y is equal to x plus Right, so I have to just now solve this I'm short of space here. So I'll go and Now solve that in the note. So just let me just rewrite the equation 300 by u 200 by v Right, so the equations are what are the equations? So the equations are 300 upon u plus 200 upon v is equal to 5.5 And then we had 260 upon u plus 240 upon v Is equal to 5.6 Okay, and then we transform these equations to 300 u plus 200 v sorry 300 x That's 200 y equals 5.5 and the second equation was 260 x plus 240 y equals to 5.6 and then Let's say this is one and this is two So do two minus one and you will get 40 y minus 40 x is equal to is equal to Is equal to 0.1 and hence I can write y minus x is equal to 0.1 by 40 Which is nothing but 1 upon 400 Right y minus x. So y y can be written as y can be written as x plus 1 by 400 Okay, and then now you can use the first equation. So using the first equation. What can I say? 300 times x plus 200 times x plus 1 by 400 Is equal to 5.5 Right substitution. I'm using so 300 x plus 200 x Plus 200 by 400 Which is half is equal to 5.5. So hence I will get 500 x Is equal to 5.5 Minus 0.5 because 200 by 400 is 0.5. So which is equal to 5 So hence x is equal to 5 upon 500 Okay, so x is 5 upon 500. So which is nothing but 1 upon 100 So what is then what was u? So u is 1 upon x Is equal to 100 kilometers per hour 100 kilometers per hour. So now when x is this much So what is y? y is equal to 1 by 100 plus 1 by 400 Because y is x plus 1 plus 400. So hence you will get 4 plus 1 by 400 Isn't it? So which is nothing but 5 by 400 which is nothing but 1 upon 80 So what is v? v is 1 upon y which is equal to 80 kilometers per hour So these are the two Speeds one is 100 kilometers per hour. Another is So you can check if it is correct. So hence 300 first equation will check 300 by 100 is 3 and 200 by So you'll check in this equation 300 by 100 is 3 and 200 by 80 is 2.5. So 3 plus 2.5 is 5.5 Looks like correct Okay So This is the This is again a bold question Next is Find the value of a for which the pair of linear equation this and this has infinitely many solutions So you know this condition again for infinitely many solutions and a1 by a2 is equal to b1 by b2 Is equal to c1 by c2 always remember for infinitely all equal Infinitely solutions all equal all ratios must be equal now What is a1 by a2? So first of all write the equations very very carefully So you can write 2x plus 3 y and hence it is equal to 7 So it is better idea to write all of them together All right, and the second one is 4x plus ay 4x plus ay Minus 14 equals to 0 So that means a1 by a2 2 by 4 must be equal to 3 by a must be equal to minus 7 by minus 14 Right, that means 1 by 2 must be equal to 3 by a And hence a is equal to 6 Right, so this is not Sorry So actually if you see this particular question was asked in cvse 2018 so this is cvse 2018 problem last year this question was asked in the board exam Okay Next yeah, so this is the question the question is the tense digit of a number is twice its units digit And the number obtained by interchanging the digits is 36 less than the original number find the original number for this is also cvse 2018 same basic to the one equation Okay, so the tense digit of a number is twice its units. This is so let's let the digital or you should write let the tense digit D x and let the units digit dy The number obtained by interchanging the digits is 36 less than the original number. So original number is original number Is nothing but what is original number? 10 x plus y and new number after Interchanging the digits Interchanging the digits will be 10 y plus x Now, what are they saying that the the number obtained by interchanging 36 less so the new number is 36 less that means The original number was 10 x plus y and if you subtract 36 from it you will get 10 y plus x Okay, and another information which was given in the very first line was the tense digit of a number is twice its units digit So hence, I know x is equal to y Isn't it? Tense digit of a number is twice its units digits. So x equals to 2 y and now simplifying this equation you will get What will you get 9 x? minus 9 y is equal to 36 And now put x equals to 2 y so you'll get 9 into 2 y minus 9 y Is equal to 36 So 18 y is equal to 36 So y is equal to 2 And x hence equals to 4 right, so Am I right? 42 and 24 is not No, something I'm sorry 4 this will be 4 this is 9 x minus 9 y is 36 so x is 2 y so 18 y oh, this is 9 y and sorry So hence this is 4 and hence it is 8 Right, so the number is 84 because If you reverse the number it will get 48 and the difference is 36 Yes So hence what is the original number original number is so don't write these things in your paper because this is just to For me to check so you can check it in your rough rough area so x is or original number Number is equal to 18 4 Okay So these are this is also cbc 2018 so you now know the you know the questions of linear equation will not be of That you know the questions will not be such that you will not be knowing it The problem general problem in linear equations You need to take care is But what should you take care of one is? Linear equation you must be very very careful in terms of calculation mistakes Most of you would be losing marks because of this Right Second this thing is re-check The solution Please re-check the solution Okay, so you can buy by deployment by deployment of the actual value Please check it. Okay third is remember the three criterion remember criteria For consistency Consistency means whether the solution is there or not remember the three can three cases So one a1 by a2 is not equal to b1 by v2 This is for one solution Right, then a1 by a2 is equal to b1 by v2 is not equal to Is not equal to is not equal to c1 by c2 This is parallel line or inconsistent and third is a1 by a2 is equal to b1 by v2 c1 by c2 infinitely many solution many This is also called no solution So, please remember These three do not get confused and do not use wrong condition then solve the question by the desired method or the or the method Mentioned These are the common errors Do not just jump on solving this equation Just after looking at the question Okay, so you please read it read the question carefully Okay, and then very importantly spare some time to go through the solution and check whether the obtained solution satisfy the given set of Okay, so I think this is good enough for you for you know for the entire summary of the chapter So I think you'll be able to solve it and the questions will be within reach Do not The only thing would be that you will be making mistakes while calculation and so do not do silly errors Please be mindful of this and I think you should be able to solve linear equations are very um, you know very low hanging fruits in your exam paper So guys if you have any other problem, you can post it here. Otherwise, I think you are good to go and So we will meeting again with the another set of Let's say another topic Okay If you have any other question, you can please post it here. Otherwise, you can always reach out to me separately So if you don't have any other queries, then we'll call it a day and then we will take up New topic tomorrow Anyone is having any problem? So thanks a lot guys. See you then tomorrow. Thank you


All right, fantastic, name of change, okay? This is now the Sakwa, okay?  You're watching Why In The Morning. This segment is about entrepreneurship and today's interesting topic is all about money. And I remember before we took our break, I had asked you, where does money come from?  So we're going to talk about that. And also the conversation just around, you know, how money works, the relationship you have with money from, you know, a banker's perspective to now as a monangy, a common monangy perspective and what not. So we're going to actually have a very interesting conversation about that and joining us live in studio with us is Edwin Masai Mushira. He is a financial consultant and he has had also an opportunity to work with some of the leading banks in Kenya including INM Bank, SBM Bank and he's also a business owner as well. So he'll tell us how he went like from working in the banking industry to becoming a business owner and much more. So take a pen and paper and come close to your TV and good morning. Good morning to you. Thank you for having me. Welcome to I2 for 4. Nice to have you. Thank you so much. Right. So we were having a conversation behind the scenes and we actually just trying to like get through a quick run through of what exactly happens when it comes to matters of money and banking to you from a professional perspective. What do you think should be the conversation starter when it comes to, you know, the conversation about money? Where should we begin from? Money is a broad conversation that's actually very, very interesting in regards to where it starts, how you're going to use, how you're going to expound it, how you're going to get people to work with it. By working with it, is it how do you get investors on board if you're doing a business? If you are working, how do you manage your finances? How do you look at what aspect of things to look at? So there are very many ways of looking at money and probably the best is how to get the money or what money is in the first place. So maybe that's why maybe we should start. So what is money? That's a good question. Where does it come from? So as we were talking about this, there was the inside joke of what is money? So bankers say money is stationary where basically we look at it as paper or as coins, so to speak. So don't look at the value of the money. Money, however, has value and value is pegged currently in Kenya by the CBK and where we are and money is a form of trade. And it depends without looking at do you want to buy shopping? Do you want to pay school fees? Do you want to buy a house? Do you want to rent out a car? So money is a means of satisfying needs and wants, yes. So basically it's like you need to have money. You can't escape. You can't go through life without it. Unfortunately, right now we can't work without money. That's why we are. And to ensure that the essentials of life are met, money is key in all this. Right, let's switch gears a little bit and talk about now. Let's say the local person, a person who is not financially literate. I remember behind the scenes we talked about, we talked about when you get your first million, how do you handle it? Are you going to spend it? And you mentioned your spending habits. For example, a student, a campus student, let's use example for campus student, you've just been given 700,000. How do you actually plan from that money so that at the end of the day you have something meaningful out of it? In as much as years you're going to spend it, of course money is meant to be spent or served and any other thing that happens to eat. Now from a person that should be maybe, let's say, have some form of understanding or the dynamics of how to actually handle that, where do they begin from? That's a brilliant question. Where do you start? The better question is where do you start with the shilling? Everything is on principles, principles of money. How do you handle money? How do you handle your needs? There's a basic rule where you split the money into three ways, 50%, 30% and 20%. Also it's 50, 30, 20 rule. Yes. Wow. So... She'll explain. Yes. So 50%, basically this goes back to the conversation where we had when your kids, what are needs, what are wants and how can you split in between two. So let me start. So needs are essential that you cannot do without. And wants are things or items or activities that can better your life. And that aspect will be savings. So in the 50%, that's where you spend on your needs, that's on your house rent. If it is a student, that's where now you look at books, essentials, if you're looking at shopping, basic shopping. Then on the other hand, you look at the needs. So from there, the needs move to the wants, which is about 30%. Now for the wants, these are things that better your life. You want to better clothes, better shoes. You wanna matter too. Now you want a car. So those are things that look at wants and those things that can be able to readjust. For instance, if your wants go beyond what you're having, you can reduce them. However, the needs, those are items that you cannot reduce. For instance, you cannot reduce the amount you eat. It is, you need to eat to move. You need to pay that bus fare. It's mandatory. Indeed. So those are aspects that are really, really important to look at. So that's where the 50% goes at. For the last or the 20%, that's where you look at savings or emergency fund. It's also a small but a very broad area as well. For instance, when emergency fund, you look at medical care. If you're not an institution where you're being given medical insurance, you need to save up for it. You need to save up for retirement. That is something that people don't really look at. It's like a financial plan. Is that what we call now financial planning? Yes. So you need to have these things way, way before you have the money. Oh, you need, it's like your manifest. It's like you're planning for 10 million that you don't have. Yes, yes and no. Okay. Yes, you need to plan for what you don't have. However, you need to plan for what is adequate. Okay. So, you need to look at this. This is the level that I need to be. Those are the ones. And this is really what I need to do so that I'm able to get to this point or to survive. And then there's what you look at after. It's always said that most middle-class cadence are one disease away from poverty. How do you negate yourself from that? It is from the 20%. It is from these savings that you put across. It is not very easy to convert land buildings and cars when you have a medical emergency. You need cash. So, the instruments that you can be able to use like unit trusts, fixed deposits, simple deposits. So, there are things that you can be able to do and invest in that 20%. That really doesn't look much, but will elevate you from problems when you are in those dire problems. All right, yes. Interesting, interesting. Now, from a financial expert's perspective, of course you worked at a bank and the transaction, I'm sure there's like a many million transactions that happen in a day or maybe in an hour, especially in, you said there's tiers of banks like first, second, third. At what point in your experience, when you see a person making a transaction and you say, bro, you have bad spending habits or from the way you're spending, clearly you need something. Like you need to actually correct on your expenditure or your spending habits. What is the philosophy behind that? In banking, the various things that people look at. For starters, what you talked about, the spending habits. You bank a check together or you get an outrageous in today or you just get money, deposit your money in today. Then two hours in, it's out. That's a red flag. That means you don't have what bankers call retention. And you can retain your earnings. So if your earnings are not traceable in terms of the ruler I gave you earlier, then that's showcased as a red flag. There are individuals who actually have a lot of money but the spending habits do not correlate to the amount they have and the people who have way less money and they qualify for very huge loans. You talked about Mamambogas and at your combat and other informal or MSCs. So they usually, if they have very good spending habits or saving habits, they can get access to a lot of finance or money in terms of banking. So those are the things that you look at. And we tend to advise clients on how to mitigate this and how to help them get into this. So with the rule for instance, you can allocate like 1% or 1 to 5% of the money that came in as a retention value. So now the account becomes, they can be able to correlate with how you are able to retain your money. So it becomes easier to get facilities. All right, interesting as well. Now, I'd also like you to tell us, for example, a person who's earning, let's say 50,000, how can they ensure they retain that money to a point they're not going above it or little below it either. But I think it's good to go below it. I'd like to hear your point on that one as well. And then maybe a person who's earning a million, like what should be the expenditure plan or schedule for instance? I think in terms of money, I don't think the value or we may use the stationary term, the quantity of money that you have on earnings, should determine how you should spend. How you should spend is based on your lifestyle and how you plan your lifestyle. It's not about the amount of money, it's the lifestyle, the life you need, quality of life. Yes, interesting. So you may get, for instance, as you give an example, a person earning 50,000, they may say the money is too little, I can't get to work maybe by 20th and I'll speed on fast. I can't get my shopping right, I need to send something home and need, I need, I need. So there are so many so-called needs. There's emergencies along the way, remember? Yes. And you talked about emergency funds, you will talk about that as well. But remember, it is not the need, the need I need. There's needs and there's wants and there's savings. So just need to go back to that drawing board again. So at 50K, you realize that this particular point you can't do really much, but you need to split this with the wants and the needs and the savings. And then again, in the savings, other than just putting money aside, you can use part of that money to improve your life in terms of getting higher education, saving for higher education, saving for a better cause, saving for a course that will teach you how to do a passive income, a passive activity that raise passive income that would not affect your current active job. So these, again, will increase your savings and increase your activities therein. So you can be able to gain more from the 50K, probably to 100. The major thing that is a drawback is people talk about is pay or tax or to speak. So from the savings perspective, the aspects that you can do, like for instance, are selling about the unit trusts. These aspects, they can actually be able to cushion you on this. Because if you look at maybe like a life insurance, there's a tax rebate on that. So the more you save, the more tax rebate you get from the government and then more you have more spending amounts on your end. So the guy with the million Bob, probably it was not instant, it was again from the 50K.  Not mean, but frugal.  Again, you're sending enough money home or you're taking care of your family. At the same time, you're putting money aside for your retirement and medical. And continuously funds. Right. Thank you for that. You reminded me of something that we asked the youth, the millennials, we talk about having a steady flow of income. You know, wait until I'm financially stable. Is there anything like that by the way that having a steady flow of income and financially stable, is there anything like that? Again, it goes to the quality of life that one is looking at. At the same time, we look at various ways that one can be able to focus on. Unfortunately, the answer to that question is there's no time you will say that you're financially stable. So let's say you own a house and have a car or two. Again, you own a bigger house, you have your kids, now you have maybe grown kids, they want to go to a better school, they want to go abroad. So you'll never be stable, so to speak. So the stability all depends on how you lay down your needs and wants and again on savings. It still goes down to those basics. In the plan now. Yes, so if it works within the plan, you are perfect. If you spend more on the savings and you don't have food, you'll go back to the savings and take away the savings. So the best thing is to understand where you are and the direction that you're headed and understand that you can be able to grow your income. Maybe adding up on another positive income as well so that you can be able to add more income on your plate. Right, yes. There's a place I was reading and they were saying if you're fancy and above with your money, you should have at least two streams of income and you mentioned positive income. Now in relation to that, even in our country as well, we have, it's called debt crisis. It's like we're living on debt. Is it possible for us as a country and always narrow it down to an individual to like just live a debt-free life where you don't owe anyone, no bank, no digital money lending system and all of that. In as much as years, we want to have these SMEs. They need funding and somebody also mentioned that even the biggest businesses are surviving on debt. It's debt servicing. Talk about that as well. Debt is interesting. What I mean by interesting is let's go back to how you create money. Banks create money by giving you loans so that now you pay back in interest. Where does this money come from? When it comes from deposit that you're putting in the bank. So the bank looks at your deposit as liabilities or rather debt. Liabilities? Yes. Deposits? Yes, deposit at debt. Because they need to pay you a certain interest at the end of the year. This is debt. They owe you this money. They have borrowed, so to speak, this money. From you? From you. So when now another borrower comes and they issue the money, the income they gain from that interest is called interest income. Oh, interest income. Or on the end, it's assets. To the bank now? Yes. So that's why on the banking side, when you get your statement, it's opposite. Where you think it's your deposit, it's a credit. Because the bank views you as a liability. As a liability. Bro, that's bad news. No, that's good news for you because you earn interest.  No, not really. The bank views you as a liability.  So again, what do you deal with people who owe you money? You call them up, you talk to them nicely. That's what the bank does to you.  You have deposits that are looking nice. Please stop up, ETC, ETC, ETC. They are always on you to ensure that you are comfortable. You don't withdraw your money to get to another bank. So these are aspects that move around the debt issue. So to speak, debt is not bad, but bad debt is bad. Please explain that bad debt is bad. Like, how bad is a bad debt? For example, I don't know. We owe more than 10 trillion Kenyan shillings to our lenders, including China as well. China is one of our biggest debtors, including the IMF. I don't know if we owe the IMF, but our debt is really... We would say it's bad debt, I'm sure. What's your opinion on that? It just goes down to the numbers. Of course, everyone wants to have cheap debt or no debt at all. So high collateral debt is expensive. High collateral debt is not something you want to look at. It affects other things like inflation. So the country or the government may prefer to go to such institutions or rather external borrowing other than internal borrowing. Because internal borrowing will foster more inflation, which is bad for us. We're experiencing it right now, right? Yes. In fact, it's both internal and external now for the country. Yes. So the government is usually trying as much as possible to have external debt instead of internal debt. Because when you borrow internally, how do the government borrow internally? They have treasury bonds, T-bills, and these are flooded by the CBK or the treasury. And when this happens, if they borrow so much internally, their rates go higher. So they're usually seen as very safe investment portfolios for one to have. So if you look at something that is about 9 close to 11%, that's really, really high on a treasury bill. So this translates to banking. Because in the bank, they would rather buy those T-bills than give you money because they're sure the government will pay. That's the money you're going to pay. So when your end is going to happen, they're going to increase their rates to you so that now they can put that risk instead of giving the money to the government, they give the money to you. So that fosters inflation. That's why now the money becomes expensive. Getting loans up to 18%, 20%. Currently, we have about three banks now that have to go ahead to have risk-based pricing on loans. So we are looking at higher interest rates coming up very, very soon. So this, again, is bad for inflation. So international debt, so to speak, or external debt, is not something to look up to. By the same time, it is necessary to ensure that certain elements and infrastructure are taking place. So the only aspect is to ensure that it is well manageable in areas that you can be able to prepare. On that note, how can a person, I'm trying to find the right word in my mind, how can you, let's say, manage debt individually? Well, like managing debt, well, effectively. And literally now breaking away from it, like not living in debt kept, kept, kept, kept. Is it possible to like, for example, you borrowed, let's say you borrowed $5 million and then you tried to buy Shamba and then it came to a place, at all costs, I couldn't afford it.  How can you manage it effectively to a point is not now detrimental to any other flow of income that you have? Debt crisis, personal debt crisis is a huge, huge, huge problem. And when you're looking at debt crisis, you're looking at ways and means that you can be able to reduce this. And sometimes it is not as easy as said than done.  And then you start scheduling based on high priority to lowest priority, so to speak.  You need to reduce on your wants because needs really, there's nothing you can do about it. You can't stay without water or food. Is it possible for someone to have expensive needs? Like your needs are so expensive, they are almost translating to wants. Do you have to cut it down? Yes, that's the conversation. You need to understand what are your needs and what are your wants. And unfortunately, sometimes you need to make expensive decisions or heavy decisions. What I mean is, for instance, you're having a big car that is a Gazela and right now in debt, you need to downgrade either to a smaller car or maybe from three to one car. I mean, so you're losing the value of that car. Not really. By cutting back, you give yourself a chance to move back up faster and easier. Because now with debt, with bad debts, you can say at B, you cannot access to finance, you cannot start another business, you cannot be able to do these things. And that's why right now there's rise of so many microfinances, some are not governed. And that's why some of them get robbed because you are unbankable, so to speak, because you have very bad debt. So to ensure that does not take place, you cut back on your needs, on your expensive needs, and then push them to wants. And then now from the wants, you look at what you can let go. Then from there, now you can go back because a good example is when you have a medical crisis, you can easily go to bad debt. The emergency fund or something like that. Yes, because you can use it, you can entirely utilize it and it's over. They go back and now borrow against it, maybe a shamba or something and get into bad debt. So on such things, that's when you start cutting back and that is when you look at what works for you. All right, thank you, fantastic. Now let's switch gears a little bit to savings. The conversation should be on savings culture. We began in the mission to, for example, you're given 700,000 and all of a sudden you don't have it. Now in this generation of millennials, content creators, you want to impress literally because you're young, you're energetic and all that. Now, do you feel like we have a consistent pattern when it comes to financial literacy? And at what point should we start instilling this culture from our kids? I remember there was a time we had a conversation with a friend of mine and they were telling me, kids in Japan, as early as four years old, they're being taught how to create a keyboard, create a computer, algorithm. By the time they are mature, they are creating a company and employing other people. So it began at a very tender young age. Now, for us here in Africa, the culture is go to school, graduate, get a job, go get employed, start saving. But now how do you figure to that place that you know, yes, I'm employed or yes, I'm gonna start a business which we commonly know, I end up on the Shabia Sharaka with a part of job. How do you figure to a place that you know, you have a consistent serving pattern? That really starts from day one. By day one, I mean, as early as possible. You'd be surprised, there are so many families that instigate this in their kids. They ensure that their kids understand this. So how do you do this? There are some individuals and families and they give the kids certain goals. When they achieve certain goals, they get certain rewards. Now, when they get these rewards, they are shown the saving culture right from then. These rewards could be monetary, it could be sweets or presents. From that point is when you teach a child how to share, teach a child how to put something you can use tomorrow or the next day or a few days after. It starts from there. Then slowly as the kids age, you have seen some bring their kids to the bank and they open an account together. They show that this is what you do and they give them maybe 100 shillings or something. And then the kids come with their parents together and they bank. Those are small aspects or elements where the kids understand that actually you need to start saving. And to get rid of that aspect where when you get the money in share, it becomes very easy when you start from day one. Yes, if the child may be 100 shillings for instance and they want to buy sweets and popcorn, no, no, no, we need to put maybe 20 shillings aside. And then spend the 80 shillings on those things. So from the 80 shillings, now tell me again, now what do you think is really important? Is this or this? Do you really need this or do you want this? So you start getting that conversation really early in your life. And they should go back to again to schools. They should ensure that this is taught so that these individuals or groups, when they start early in their life and they get income, it becomes very easy for them to transition and ensure that they are free to go and not spend the rest. Right, interesting, thanks. Now for a young person who is trying to figure out life, you think so, you need money. Of course you need money. So as long as you're breathing in and out, you will need money. And those people who say, me I'll do anything for money, I don't care if it's gonna cost my soul or it's gonna cost me a person, if they have to go so that I get money, what would be your advice to someone who's watching and they want to have money? But of course the basics are get a job or start a business. Where do you pick up from scratching to that point now? Sometimes it's very difficult when you tell someone get a job and then they'll tell you, okay fine, give me that job. Sometimes you don't get home to the skills where to start looking for a job, for instance. A while back you used to look at newspapers, right now they are none or maybe they're few for starters. So where do you start? Those are the simple things, I think which is really important. And one fits all doesn't really work for everyone. And what aspects people say that need to work with what you like and how you like it to be done. Sometimes that works, but which platforms or which areas should you look at? There are various areas that people look at. There's LinkedIn which is right now quite autonomous. But autonomous I mean it is very diverse. Where you can get a lot of passive and still active or hybrid solutions or other jobs. So this is where you start. So from small things that's where you start and by identifying what is the gap and what you're really good at. That's where basically you start. Right, let's also now switch gears as well to the digital markets. And I'd also like you to talk about the digital one less now. Because we are in a generation of tech. Almost right now every kid who is in school they are being taught to be tech savvy. It's like among the first skills that you should have. Now in a generation where there's forex trading, people being scammed left, right and center. Oh, CG, I'm 12 years old with your boards. Oh, I compare 10,000, say easy, I tell you account, how do we actually manage this to a point that we have like now certified professionals and even investment platforms that for example, if I'm giving you 10,000 you'll be able to be accountable for that. Just in case maybe you're trading on my behalf. Because right now I understand banks are also regulating forex. There's banks that are actually coming to actually help or assist people or even they're also offering that. How can someone reach and hit that pinnacle off? You know having like it's professional, I'm doing it professionally, I'm not being scammed. I'm gonna get my money right and I'm gonna hold you accountable as well. Regulation is key and government institutions need to do their bit in terms of regulations to ensure the right institutions and companies are working on board on this to ensure that Kenyans don't get scammed. However as Kenyans research is a key element in doing this and there are so many ways one can be able to do research and sometimes it doesn't hurt to consult someone. Even consult your banker, consult your financial consultant, consult someone who is in that business. So they can be able to give you some advice on what works what doesn't work. Again. But how do you know decipher?   How can someone decipher for a person but I'm sure it's possible for someone to work at the bank and scum someone. They'd be like no, they disappeared, they're no longer there. Is it possible for someone to like have a trusted professional to handle their business financially? Yes, there are institutions that actually work on that professionally. However, sometimes it is best to go the traditional way. Yes, we are modern, but it's best to go traditional for instance. If you pick elements like unit trusts or if it is forex you're going to banks or such elements, it is very easy to trace back. And if you look at companies or institutions that are publicly audited, it becomes very, very easy for you to know their trustworthiness and establish where they are. A good example, sometimes is not a good example. Let me give you an example. When you talk about liabilities, there are some clients who come on board and they want to put a good fixed deposit probably 100 on 50. And the question they ask, what's your portfolio? What's your value? What does your bank hold? How much does your bank hold? They don't want to put their money in elements or in institutions that can actually go down maybe in a year or two. So even them, for people who are coming to bank for about 150 million, they still ask those pertinent questions. They still go back to the audited statements. They still go back to the traditional way of ensuring that their money is safe. So at the same time, when you look at digital markets, they are, it's broad as well and there are so many elements. There's so many elements in terms of good elements or good channels that one can actually make good money and they should be well exploited. I think additionally, using certain instruments in banks can be able to shell view from cons. For instance, if you have a bank being an intermediary where the person offering the service, they're putting the money first and then you get assured that you get the money once the service is done, such instruments can be able to assist you in ensuring that this transaction is solid, this transaction cannot be a con. Right. Yes. Oh my goodness. I'm being told I have two minutes to wrap up, but I would have asked you about how can someone boost their credit score, but it's okay. Briefly talk about your business and what you do and just in case you're offering any services and also your financial consultancy services, how can a person reach out and get in touch with you? There's a number as well. Please share with us in a minute. Sure. So basically, I'm a financial consultant. I focus on working capital solutions where I showcase individuals and groups and companies on how to get working capital for the entities to move them and to foster their growth and their activities. So the best way to reach me is through social hurdles and through my phone numbers. Yeah, please. That's your camera. All right. So my phone number is 0726-800-594. And my social network Twitter is at Edie Masai, Instagram Edwin Masai, and Facebook at Edwin Masai. Yeah, please repeat the number once again. If you have issues to do with money, do you want to retain your money? You want to retain your salary? Ataka Maniki Dogo. If you want the tricks, please contact Edwin. Please say the number once again so that people can get it right. 0726-800-594. All right. Thank you so much, Edwin. I think we should have a part two of this conversation because it's an endless conversation. Sure. And I had so many questions. So we're going to take a very short break, but we'll be coming back with much more. We have been speaking to Edwin Masai Mishira, who is a financial consultant. I would really love to hear how you transition from working in the banking sector to now the business, but you tell us next time as well. And thank you so much for your insights and your time and for coming through. Thank you so much for having me. You're welcome. So we take a very short break. We come back with much more. Continue to interact with us on that hashtag Why In The Morning, Entrepreneurship Tuesday, at Y2 for 4 Channel, at Brian Soko 101, and at... Edwin Masai. Edwin Masai on Instagram, as well as Twitter and Facebook.


One year ago, we announced our first SM32 microprocessor. We are very excited in ST Microelectronics to address microprocessor's application with our SM32MP1 product and to enable innovation and creativity for customers and partners. Today, we are broadoning the SM32MP1 product series with just announced yesterday a new SM32MP1 now supporting 800MHz on the Dual ARM Cortex A7 while keeping software and pin-to-pin compatibility with the 650MHz version. Thanks to this performance boost, we will better address applications where all support is key. To them a few, HD video decoding, voice and audio processing, more powerful artificial intelligence for neural network and machine learning applications and better user experience in Android system. In terms of application, we could think about a smart home gateway where Dual ARM Cortex A7 at 800MHz would enable HD video decoding for double, 3D GPU for advanced graphical user interface controlled by voice, and sensor acquisition handled by Cortex M4 with time domain. Now, I talk about the smart home gateway application but don't forget the SM32MP1 is a multi-market microprocessor focusing on industrial smart home smart city health and wellness. Industrial applications are most probably the most demanding in terms of specification. We did a dedicated qualification with 100% operating time during 10 years combined with minus 40 to 125 degrees junction temperature. This is really key for an industrial application. In addition, industrial customers require longer product lifetime and to address this, we are keeping our 10 years on JVT commitment program renewed every year. SM32MP1 supports industrial connectivity, advanced analog, ARM Cortex M4, real-time domain and advanced security for industry fall at home.


Copper nanoparticles have become increasingly popular in recent years due to their potential applications in printed electronics. However, their use is limited by their tendency to oxidize in ambient conditions. Several methods have been developed to coat copper nanoparticles with protective layers to prevent this from happening, including organic polymers, alkene chains, amorphous carbon, graphene, and inorganic materials like silica and metals. These coatings allow for the formation of high conductivity patterns when used in conjunction with inkjet printing techniques. The use of copper nanoparticles in printed electronics opens up new possibilities, such as the production of RFID tags, solar cells, and electroluminescent devices. This article was authored by Shlomo Magdasi, Alexander Kamyshny, and Michael Grouchko.