Question

Solve the system by substitution
-x - y - z = -8
-4x + 4y + 5z = 7
2x + 2z =4

Answer 1

2 x + 2 z = 4 Divide both sides by 2

x + z = 2 Subtract z to both sides

x + z - z = 2 - z

x = 2 - z


Replace x = 2 - z in equation - x - y - z = - 8


- x - y - z = - 8

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

- 2 + z - y - z = - 8

- 2 - y + z - z = - 8

- 2 - y = - 8 Add 2 to both sides

- 2 - y + 2 = - 8 + 2

- 2 + 2 - y = - 8 + 2

- y = - 6 Multiply both sides by - 1

y = 6


- 4 x + 4 y + 5 z = 7

Replace x = 2 - z and y = 6 in this equation

- 4 * ( 2 - z ) + 4 * 6 + 5 z = 7

- 4 * 2 - 4 * ( - z ) + 24 + 5 z = 7

- 8 + 4 z + 24 + 5 z = 7

- 8 + 24 + 4 z + 5 z = 7

16 + 9 z = 7 Subtract 16 to both sides

16 + 9 z - 16 = 7 - 16

16 - 16 + 9 z = 7 - 16

9 z = - 9 Divide both sides by 9

z = - 1

Replace this value in equation x = 2 - z


x = 2 - z = 2 - ( - 1 ) = 2 + 1 = 3


The solutions are:

x = 3

y = 6

z = - 1