4x+7y-z=42, -2x+2y+3z=-26, 2x-3y+5z=10?

Answer 1

I assume you want to solve this system of equations:

A) 4x + 7y - z = 42
B) -2x + 2y + 3z = -26
C) 2x - 3y + 5z = 10

I'd add B and C to eliminate the x term:
2y - 3y + 3z + 5z = -26 + 10
D) -y + 8z = -16

Now double B and add it to A to eliminate x from those equations:
A) 4x + 7y - z = 42
2B) -4x + 4y + 6z = -52
E) 11y + 5z = -10

So you have two equations (D & E) with just y and z:

Now multiple D by 11 and add to E to eliminate y:
11D) -11y + 88z = -176
E) 11y + 5z = -10
93z = -186
z = -2

Now substitute z back into E:
11y + 5(-2) = -10
11y -10 = -10
11y = 0
y = 0

Finally plug y and z back into A:
A) 4x + 7(0) - (-2) = 42
4x + 2 = 42
4x = 40
x = 10

Answer:
x = 10, y = 0, z = -2

Answer 2

4x+7y-z=42, -2x+2y+3z=-26, 2x-3y+5z=10=
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