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