Answer
$$x=2,\:y=\frac{1}{2},\:z=-2$$
Work Step by Step
Solving the system of equations using Matrices, we find:
$$ \begin{bmatrix}3&2&2&¦&3\\ 1&2&-1&¦&5\\ 2&-4&1&¦&0\end{bmatrix}\\ \begin{bmatrix}1&0&0&¦&2\\ 0&1&0&¦&\frac{1}{2}\\ 0&0&1&¦&-2\end{bmatrix}\\ x=2,\:y=\frac{1}{2},\:z=-2$$