First, we add the first and third equations to get -x+3z=8. Then, we multiply the first equation by two and add the third equation to that to get 3y+5z=9. Then, we subtract that from the second equation to get -3x-2y=1. Then, we add the first equation to the second and subtract the third equation from that to get 7y+6z=4. This means that we now have the equations

-x+3z=8

3y+5z=9

-3x-2y=1

7y+6z=4

Looking at the second and fourth equations, we find that y = **-2** and that z = **3**. Solving for x, we find that x = **1.** I'll leave the checking up to you.