We use cramer's rule here.
The matrix form of the system is
[tex]\begin{bmatrix}{1} & {1} & {3} \\ {-3} & {7} & {-2} \\ {7} & {-6} & {-5}\end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {z} & & \end{bmatrix}=\begin{bmatrix}{12} & {} & {} \\ {-35} & {} & {} \\ {32} & & \end{bmatrix}[/tex]The matrix A_x is found by replacing the first column of
