The given system of equations is:

5x + 2y = 3

3x + 2y = 5

The given system of equations can be written in the form of AX = B, where

Now |A| = 5(2)-2(3) = 4 ≠ 0

∴ A is a non-singular matrix and hence A^-1 exists.

Now

AdjA =

So

And

So

Hence x = -1 and y = 4