Your system of equations is
[tex]\left[ \begin{array}{ccc}1&1&0\\2&0&-1\\0&1&-3\end{array}\right]\cdot \left[ \begin{array}{c}x\\y\\z\end{array} \right] = \left[ \begin{array}{c}10\\9\\-5\end{array} \right][/tex]
Then the solution is
[tex]\left[ \begin{array}{c}x\\y\\z\end{array} \right] = \left[ \begin{array}{ccc}1&1&0\\2&0&-1\\0&1&-3\end{array}\right]^{-1}\cdot \left[ \begin{array}{c}10\\9\\-5\end{array} \right][/tex]
Your graphing calculator or any of several web sites can compute the inverse matrix for you.
[tex]\left[ \begin{array}{c}x\\y\\z\end{array} \right] = \dfrac{1}{7}\cdot \left[ \begin{array}{ccc}1&3&-1\\6&-3&1\\2&-1&-2\end{array}\right]\cdot \left[ \begin{array}{c}10\\9\\-5\end{array} \right] = \left[ \begin{array}{c}6\\4\\3\end{array} \right][/tex]
The solution is (x, y, z) = (6, 4, 3).
