The given system of equations is:

5x + 2y = 4

7x + 3y = 5

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

Now |A| = 3(5)-2(7) = 1 ≠ 0

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

Now

So

And

So

Hence x = 2 and y = -3.