System of equations? BEST answer to first correct

x - 2y - z = -4
-x + 6y - 3z = 12
2x - 11y + 5z = -22

Please solve for x, y, and z.
Thank you vedddy much!

x = 0
y = 2
z = 0
Rearrange 2nd equation
-x + 6y - 3x + x - 12 = 12 + x - 12
6y - 3z - 12 = x

Substitute x into the 1st equation
(6y - 3z - 12) - 2y - z = -4
4y - 2z = 8, we can simplify this to
2y - z = 4

Rearrange equation

2y - 4 = z
Substitute x into the 3rd equation
2(6y - 3z - 12 = x) - 11y + 5z = -22
12y - 6z - 24 - 11y + 5z = - 22
y - z - 24
y - z = 2

Substitute z into that equation
y - (2y - 4) = 2
y - 2y + 4 = 2
-y = -2
y = 2

Substitute y = 2 into y - z = 2
2 - z = 2
-z = 0
z = 0

Substitute x an y into 6y - 3z - 12 = x
6(2) - 3(0) - 12 = x
12 - 0 - 12 = x
0 = x

x = 0
y = 2
z = 0

{0, 2, 0}