Question

Solve the system by substitution

-x-y-z= -8

-4x+4y+5z= 7

2x+2z= 4

Answer 1

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

Explanation:

2x+2z=4

2x=4-2z

X=2-z

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

-2+z-y-z=-8

-2-y=-8

-2+y=-8+y

-2+8=y

6=y

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

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

9z=8-24+7

9z=-9

Z=-1

2x+2z=4

2x+2 (-1)=4

2x-2=4+2

2x=6

X=3

x=3 y=6 z=-1

Answer 2

- x - y - z = - 8 ------- (1)
- 4x + 4y + 5z = 7 -------- (2)
2x + 2z = 4 --------- (3)

From (3): x + z = 2
x = 2 - z --------- (4)

Substitute (4) into (1),
- x - y - z = - 8
- (2-z) - y - z = - 8
- 2 + z - y - z = -8
- 2 - y = - 8
2 + y = 8
Therefore, y = 6

Substitute y = 6 and (4) into (2),
- 4x + 4y + 5z = 7
- 4(2 - z) + 4(6) + 5z = 7
- 8 + 4z + 24 + 5z = 7
9z + 16 = 7
9z = - 9
Therefore, z = - 9

Substitute z = - 9 into (4),
x = 2 - z
x = 2 - (-9)
x = 2 + 9
Therefore x = 11

Solution:
x = 11
y = 6
z = -9