Solve the following system of equations by matrix method:

5x + 7y + 2 = 0


4x + 6y + 3 = 0

The above system of equations can be written as


or AX = B


Where A = B = and X =


|A| = 30 – 28 = 2


So, the above system has a unique solution, given by


X = A – 1B


Let Cij be the cofactor of aijin A, then


C11 = (– 1)1 + 1 6 = 6


C12 = (– 1)1 + 2 4 = – 4


C21 = (– 1)2 + 1 7 = – 7


C22 = (– 1)2 + 2 5 = 5


Also, adj A =


=


A – 1 =


A – 1 =


Now, X = A – 1B





Hence, X = Y =


1