There are many methods for solving systems, and
I don't know which way you are studying. I don't want 
to waste time solving them all the different 
possible ways which you aren't studying, so I'll just
give the solution:

(x,y,z) = (-5,-2,3)

If you want us to help you with solving it, please
tell us which of the many ways you are studying, probably
one of these:

1. Substitution
2. Elimination
3. Cramer's rule (determinants)
4. Triangular method with back substitution
5. Partial Gaussian elimination with matrices and back substitution 
6. Complete Gaussian elimination with matrices
7. The inverse matrix method, sometimes called the AX=B method

Edwin