Solve the system by substitution(show your work)

-x - y - z = -8
-4x + 4y + 5z = 7
2x + 2z = 4

x = 3 , y = 6 , z = -1

Step-by-step explanation using substitution:

Solve the following system:

{-x - y - z = -8

-4 x + 4 y + 5 z = 7

2 x + 2 z = 4

In the first equation, look to solve for x:

{-x - y - z = -8

-4 x + 4 y + 5 z = 7

2 x + 2 z = 4

Add y + z to both sides:

{-x = -8 + y + z

-4 x + 4 y + 5 z = 7

2 x + 2 z = 4

Multiply both sides by -1:

{x = 8 - y - z

-4 x + 4 y + 5 z = 7

2 x + 2 z = 4

Substitute x = 8 - y - z into the second and third equations:

{x = 8 - y - z

4 y - 4 (8 - y - z) + 5 z = 7

2 (8 - y - z) + 2 z = 4

4 y - 4 (8 - y - z) + 5 z = 4 y + (-32 + 4 y + 4 z) + 5 z = -32 + 8 y + 9 z:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

2 (8 - y - z) + 2 z = 4

2 (8 - y - z) + 2 z = (16 - 2 y - 2 z) + 2 z = 16 - 2 y:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

16 - 2 y = 4

In the third equation, look to solve for y:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

16 - 2 y = 4

Subtract 16 from both sides:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

-2 y = -12

Divide both sides by -2:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

y = 6

Substitute y = 6 into the second equation:

{x = 8 - y - z

9 z + 16 = 7

y = 6

In the second equation, look to solve for z:

{x = 8 - y - z

9 z + 16 = 7

y = 6

Subtract 16 from both sides:

{x = 8 - y - z

9 z = -9

y = 6

Divide both sides by 9:

{x = 8 - y - z

z = -1

y = 6

Substitute z = -1 into the first equation:

{x = 9 - y

z = -1

y = 6

Substitute y = 6 into the first equation:

{x = 3

z = -1

y = 6

Collect results in alphabetical order:

 {x = 3 , y = 6 , z = -1

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