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 ^{– 1}B

Let C_ij be the cofactor of a_ijin 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 ^{– 1}B

Hence, X = Y =