Answer
$$x=4,\:y=-8,\:z=10$$
Work Step by Step
Solving the equations using matrices, we find:
$$ \begin{bmatrix}1&4&3&¦&2\\ 2&1&1&¦&10\\ -1&1&2&¦&8\end{bmatrix}\\ \begin{bmatrix}1&0&0&¦&4\\ 0&1&0&¦&-8\\ 0&0&1&¦&10\end{bmatrix}\\ x=4,\:y=-8,\:z=10$$