For how many values of $\alpha $ does this system of equations have infinitely many solutions ?

$\left(\begin{array}{ccc}2& 1& -4\\ 4& 3& -12\\ 1& 2& -8\end{array}\right)\left(\begin{array}{c}x\\ y\\ z\end{array}\right)=\left(\begin{array}{c}\alpha \\ 5\\ 7\end{array}\right)$

$\left(\begin{array}{ccc}2& 1& -4\\ 4& 3& -12\\ 1& 2& -8\end{array}\right)\left(\begin{array}{c}x\\ y\\ z\end{array}\right)=\left(\begin{array}{c}\alpha \\ 5\\ 7\end{array}\right)$