solve the system by Gauss-Jordan elimination

Solve the following system:
{2 z = -8
x+y+z = -1
x+z = -5
Express the system in matrix form:
(0 | 0 | 2
1 | 1 | 1
1 | 0 | 1)(x
y
z) = (-8
-1
-5)
Write the system in augmented matrix form and use Gaussian elimination:
(0 | 0 | 2 | -8
1 | 1 | 1 | -1
1 | 0 | 1 | -5)
Swap row 1 with row 2:
(1 | 1 | 1 | -1
0 | 0 | 2 | -8
1 | 0 | 1 | -5)
Divide row 2 by 2:
(1 | 1 | 1 | -1
0 | 0 | 1 | -4
1 | 0 | 1 | -5)
Subtract row 1 from row 3:
(1 | 1 | 1 | -1
0 | 0 | 1 | -4
0 | -1 | 0 | -4)
Multiply row 3 by -1:
(1 | 1 | 1 | -1
0 | 0 | 1 | -4
0 | 1 | 0 | 4)
Swap row 2 with row 3:
(1 | 1 | 1 | -1
0 | 1 | 0 | 4
0 | 0 | 1 | -4)
Subtract row 2 from row 1:
(1 | 0 | 1 | -5
0 | 1 | 0 | 4
0 | 0 | 1 | -4)
Subtract row 3 from row 1:
(1 | 0 | 0 | -1
0 | 1 | 0 | 4
0 | 0 | 1 | -4)
Collect results:
Answer: |x = -1     y = 4     z = -4