Examine the consistency of the system of equations.

5x – y + 4z = 5

2x + 3y + 5z = 2

5x – 2y + 6z = –1

The given system of equations is:

5x - y + 4z = 5

2x + 3y + 5z = 2

5x - 2y + 6z = -1

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

Now |A| = 5(18+10) + 1(12-25) + 4(-4-15) = 51 ≠ 0

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

So, The system of equations will be consistent.