Answer
$(-1, 2, -3)$
Work Step by Step
1. Multiply the 1st equation by 3 and add to the 2nd to get $5x+5y=5$ or $x+y=1$
2. Take the difference of the 2nd and 3rd equations to get $x-y=-3$
3. Add the above two equations to get $2x=-2$, thus $x=-1$
4. Thus we have $y=1-x=2, z=x+2y-6=-3$ and the solution $(-1, 2, -3)$
