system

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.