Examine the consistency of the system of equations.

2x – y = 5

x + y = 4

The given system of equations is:

2x - y = 5

x + y = 4

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

Now |A| = 2(1)-1(-1) = 3 ≠ 0.

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

So, The system of equations will be consistent.