Consider the system below that has the solution (2, - 3), where A, B, C, D, E, and F are non-zero real numbers

a b][x1] = [f]

[c d][x2] ... [g]

Since the system is consistent, it means there are solutions for x1 and x2.

This implies that the matrix:

[a b]

[c d]

is invertible.

Since the matrix is invertible, its determinant must be non-zero.

Hence, we have the relationship ad - bc = / = 0