177. Any of the methods which have been given for
the solution of simple equations containing two unknown
quantities may be extended to those containing three or
more unknown quantities.
( 3^+ y+ «= ^)
1. Given < x -\- 2 y -\- S z = li \ to find x, y, and z.
(Sa;— y-\-4.z—U)

By multiplying equation
(1) by 3, we obtain equa-
tion (4), and by subtracting
(1) from (2), and (4) from
(3), we have (5) and (6),
equations containing only
two unknown quantities.
Multiplying (e) by 2, and
subtracting the product (7)
from (5), give_ (8), an equa-
tion containing only one un-
known quantity, y. Dividing
(8) by 9, we have (9), or
y =2. Substituting 2 for y
in (5) gives (10), and re-
ducing, we have (12), or
z i= 3. Substituting 2 for y,
and 3 for z in (1), and re-
ducing, we have (14), or a; = 1.
Explain the operation,



OPERATION.
«+ y-\- "■=


6


(1)


a; + 2y-f-32: =


14


(2)


3a;— y-\-A.z=.
13


(3)


3a;-f-3y-f-3z =


18


W


y + 2z =


8


(5)


— 4y+ z = -


- 5


(6)


— 8y + 2« = -


-10


0)


9y =


18


(8)


y =


2


(9)


24-2» =


8


(10)


20 =


6


(11)


z =


3


(12)


a; + 2 + 3-=


6


(13)


X =


1


(14)



X





53




y —


■ z


X


=


lot




2.V-


Zz


X


=


IST




3y-


,4z



154 ELEMPNTAEY ALGEBRA.
2. Given U + 2y + 3z = lOt j ^^ ^^^ ^_

OPERATION.
