Answer
$$x=-1,\:y=2,\:z=-2$$
Work Step by Step
Solving the system of equations using Matrices, we find:
$$ \begin{bmatrix}1&2&-3&¦&9\\ 2&-1&2&¦&-8\\ 3&-1&-4&¦&3\end{bmatrix}\\ \begin{bmatrix}1&0&0&¦&-1\\ 0&1&0&¦&2\\ 0&0&1&¦&-2\end{bmatrix}\\ x=-1,\:y=2,\:z=-2$$