Which ordered triple is a solution of this system 2x+y-z=7

-x-2y+4z=-15

x+2y-5z=17

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.