Examine the consistency of the system of equations.

x + 2y = 2

2x + 3y = 3

The given system of equations is:

x + 2y = 2

2x + 3y = 3

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

Now |A| = 3(1)-2(2) = -1 ≠ 0.

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

So, The system of equations will be consistent.