Question

In the solution to this system, what is the value of z?

15 points!

−3x+y+z=−1

2x+y−z=−4

x−y+z=7

Answer 1

-3x+y+z=-1, 2x+y-z=-4, x-y+z=7 getting sums
-x+2y=-5, 3x=3, from the second we can easily see:
x=1, which makes -x+2y=-5 become:
-1+2y=-5, 2y=-4, y=-2, making x-y+z=7 become:
1--2+z=7
1+2+z=7, z=4
So the solution to the system of equations is:
(1,-2,4)