I would write these as matrices:
and then row reduce to find .
If you don't know how to do row reduction, how about substitution?
Take the second equation and solve it for z:
Now insert this value of z into the other two equations:
So we need to solve
Now solve the bottom equation for y:
and insert this value into the top equation:
So we have
or
.
Thus
and
Thus the solution to the system is (x, y, z) = (2, -1, 0).
-Dan