Find the value of a so that the system has no solutions.
y = 11x + 14
2x - 4 = ax + 7 - 3x
+9674 The system is equivalent to
\(\begin{bmatrix}11&-1\\a-5&0\end{bmatrix} \begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}-14\\-11\end{bmatrix}\)
The system has no solutions when the determinant of \(\begin{bmatrix}11&-1\\a-5&0\end{bmatrix}\) is 0.
\(\det \begin{bmatrix}11&-1\\a-5&0\end{bmatrix} = 0\\ -(a - 5) = 0\\ \boxed{a = 5}\)
Therefore, the system has no solutions when a = 5.
