Subtract the second equation from the third one. This gives you 5X +3Y - Z = -9
Add this to the first original equation. This gives you:
6Y = -24 since the X and Z terms cancel out.
Y = -4
Replace the Y value in the fir equation and second equation with -4. Now you have:
-5X -12 + Z = -15 and
10X -8 + 8Z = 18
Multiply the first one of these new equations by -8. This gives you :
40X +96 -8Z = 120. Subtract 96 from both sides. Now it is
40X - 8Z = 24 Add this to your new equation 2 like this:
40X - 8Z =24
10X + 8Z = 26 Addition of these two gives you
50X = 50 since the Z terms equal to zero.
Now X = 1
Substitute X = 1 and Y = -4 into the top original equation: -5 -12 +Z = -15 to get Z = 2
So X = 1, Y = -4, and Z = 2
Check that your complete solution satisfies all three equations. It does. That's it!