Question

How do you solve `2x +y +z = 9`, `x +2y -z = 6`, `3x -y +z = 8`?

Answer 1

2x + y + z = 9 (1)
x + 2y - z = 6 (2)
3x - y + z = 8 (3)

(1) + (2) --> 3x + 3y = 15 --> x + y = 5 --> y = (5 - x)
(2) + (3) --> 4x + y = 14 --> 4x + (5 - x) = 14 --> 3x = 9 --> x = 3
y = 5 - x = 5 - 3 = 2
(3) --> z = 8 - 3x + y = 8 - 9 + 2 = 1.

Check:
(1) --> 3.(3) - 2 + 1 = 8. Correct.