Solve the following system of equations by matrix method:

5x + 2y = 3

3x + 2y = 5

The above system of equations can be written as

or AX = B

Where A = B = and X =

|A| = 10 – 6 = 4

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} 2 = 2

C₁₂ = (– 1)^{1 + 2} 3 = – 3

C₂₁ = (– 1)^{2 + 1} 2 = – 2

C₂₂ = (– 1)^{2 + 2} 2 = 5

Also, adj A =

=

A ^{– 1} =

A ^{– 1} =

Now, X = A ^{– 1}B

Hence, X = Y = 4