Solve the system by substitution, include work

For this question you are going to want to isolate a different variable in one of the first two and the third. Then you will plug those values into each other and then the reuslts into the third (I will show later). I will be using the 1st and the 3rd because those are the easiest.
-x-y-z = -8> add y and z to both sides
-x = y + z - 8 > Divide both sides by -1
x = -y - z + 8

2x + 2z = 4 > Divide both sides by 2
x + z = 2 > Subtract x from both sides
z = -x + 2

x = -y - (-x + 2) + 8 > Now reisolate x by first simplying
x = -y + x -2 + 8 > Add
x = -y + x + 6 > Subtract x from both sides and add y to both sides
y = 6

Plug the values for y and z into the second equation and isolate x.
-4x + 4(6) + 5(-x+2) = 7 > Simplify
-4x + 24 -5x +10 = 7 > Combine like terms
-9x + 34 = 7 > Subtract 34 from both sides
-9x = -27 > Divide both sides by -9
x = 3

Plug x into the thirs equation and isolate z
2(3) + 2z = 4 ---> Simplify
6 + 2z = 4 > Subtract 6 from both sides
2z = -2 > Divide both sizes by 2
z = -1

Final Answers:
x = 3
y = 6
z = -1

Optional - Check your answer by plugging the values above back into the 1st equation.

-x-y-z = -8
-(3)-(6)-(-1) = -8
-3 - 6 + 1 = -8
-8 = -8

Hope this helps!