Which ordered triple is a solution of this system? 2x+y-z=7 -x-2y+4z=-15 x+2y-5z=17

To answer this item, we express the y in the first equation in terms of the other variables. This is,
     y = 7 + z - 2x
Then, substitute the y's in the second and third equation with that of the expression derived in the first equation.

(2)   -x - 2(7 + z - 2x) + 4z = -15

Simplifying,
       -x - 14 -2z + 4x + 4z = -15

Simplifying further,
     3x + 2z = -1

(3) x + 2(7 + z - 2x) - 5x = 17

Simplifying,
     x + 14 + 2z - 4x - 5x = 17

Simplifying further,
    -3x - 3z = 3

The equations derived are,
    3x  + 2z = -1
      x + z = -1

The values of x and z in the equation are 1 and -2, respectively. To solve for y,

    y = 7 + (-2) - 2(1) = 3

ANSWERS: x = 1, y = 3, and z = -2