Answer
$$x=3,\:y=1,\:z=-2$$
Work Step by Step
Solving the equation using Matrices, we find:
$$ \begin{bmatrix}1&3&-3&¦&12\\ 3&-1&4&¦&0\\ -1&2&-1&¦&1\end{bmatrix} \\ \begin{bmatrix}1&0&0&¦&3\\ 0&1&0&¦&1\\ 0&0&1&¦&-2\end{bmatrix}\\ x=3,\:y=1,\:z=-2$$