Question

Solve the following system of equations for all three variables.
minus, x, plus, y, minus, z, equals, 1
−x+y−z=
1
minus, x, plus, 7, y, plus, 5, z, equals, 1
−x+7y+5z=
1
x, plus, 7, y, plus, 7, z, equals, minus, 9
x+7y+7z=
−9
Answer
Attempt 1 out of 2

Answer 1

The system
- x + y - z = 1
- x + 7y + 5z = 1
x + 7y + 7z = -9

Add the first and third equations: (-x+y-z)+(x+7y+7z)=1+(-9) ⇒ 8y+6z=-8 ⇒ 4y+3z=-4.
Subtract the first from the second: (-x+7y+5z)-(-x+y-z)=1-1 ⇒ 6y+6z=0 ⇒ y+z=0 ⇒ y=-z.

Plug y=-z into 4y+3z=-4: 4(-z)+3z=-4 ⇒ -z=-4 ⇒ z=4, so y=-4. From x+7y+7z=-9: x+7(-4)+7(4)=-9 ⇒ x=-9.

Solution: (x,y,z)=(-9,-4,4).