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

x = 1, y = 3, z = -2.