However, if A equals zero, then there is no unique solution under this technique in which "A" and "B" are determinants.  
When using it on a larger scale, the expansion by minors method is extremely helpful but can get tedious.  Given a hypothetical system of n simultaneous linear equations in n unknowns, it could give a solution of "x sub I" equals "B sub I" divided by "A," where "I" equals one, two, three, etc.  However, if A equals zero, then there is no unique solution under this technique in which "A" and "B" are determinants.  FTP, name this algebraic method for solving two-variable linear equations by means of determinants and named for a British mathematician.
When using it on a larger scale, the expansion by minors method is extremely helpful but can get tedious.  
Cramer's Rule