Question

x + 2y - 3z = 5

x - y + 2z = -3

x + y - z = 2


(0, 1, -1)


No Solution


(1, 1, 0)


(5, -3

Answer 1

The system has the unique solution (x,y,z) = (0, 1, -1).

Work (elimination):
(1) x + 2y - 3z = 5
(2) x - y + 2z = -3
(3) x + y - z = 2

(1) − (2): 3y − 5z = 8
(2) − (3): −2y + 3z = −5

Solve those two: from them z = −1, y = 1. Then x + 1 − (−1) = 2 ⇒ x = 0.

Check: For (0,1,−1),
1) 0 + 2(1) −3(−1) = 2 + 3 = 5
2) 0 −1 +2(−1) = −1 −2 = −3
3) 0 +1 −(−1) = 2

So (0,1,−1) is the correct choice.