Answer:
ad − bc ≠ 0
Step-by-step explanation:
If we write this system in matrix form:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x_{1}\\x_{2}\end{array}\right]= \left[\begin{array}{c}f\\g\end{array}\right][/tex]
"Consistent" means there exists a solution for x₁ and x₂. That means the coefficient matrix must be invertible. For that to be true, the determinant cannot be 0.
[tex]\left|\begin{array}{cc}a&b\\c&d\end{array}\right| \neq 0\\ad-bc\neq 0[/tex]
