We want to solve
2x + y - z = 7 (1)
-x - 2y + 4z = -15 (2)
x + 2y - 5z = 17 (3)
Add (2) and (3).
-x - 2y + 4z + (x + 2y - 5z) = -15 + 17
-z = 2
z = - 2
Therefore, (1) and (2) become
2x + y - (-2) = 7
2x + y = 5 (4)
-x - 2y + 4(-2) = -15
-x - 2y -8 = -15
-x - 2y = -7
Multiply by 2.
-2x - 4y = -14 (5)
Add (4) and (5).
2x + y + (-2x - 4y) = 5 - 14
-3y = -9
y = 3
From (4), obtain
2x + 3 = 5
2x = 2
x = 1
Answer: x = 1, y = 3, z = -2.
