Someone please help me to find the z-value
z = 5
It usually works well to do what the problem statement tells you. We don't have access to your matrix tool, so we've used a calculator instead. (See attached.)
Of course, the augmented matrix looks like ...
[tex]\left[\begin{array}{ccc|c}-1&2&2&3\\3&1&-1&2\\2&1&1&9\end{array}\right][/tex]