Solve the system, if possible.

Solve the following system:
{x+y = 9
y+z = 2
2 x-z = 8
Express the system in matrix form:
(1 | 1 | 0
0 | 1 | 1
2 | 0 | -1)(x
y
z) = (9
2
8)
Write the system in augmented matrix form and use Gaussian elimination:
(1 | 1 | 0 | 9
0 | 1 | 1 | 2
2 | 0 | -1 | 8)
Swap row 1 with row 3:
(2 | 0 | -1 | 8
0 | 1 | 1 | 2
1 | 1 | 0 | 9)
Subtract 1/2 × (row 1) from row 3:
(2 | 0 | -1 | 8
0 | 1 | 1 | 2
0 | 1 | 1/2 | 5)
Multiply row 3 by 2:
(2 | 0 | -1 | 8
0 | 1 | 1 | 2
0 | 2 | 1 | 10)
Swap row 2 with row 3:
(2 | 0 | -1 | 8
0 | 2 | 1 | 10
0 | 1 | 1 | 2)
Subtract 1/2 × (row 2) from row 3:
(2 | 0 | -1 | 8
0 | 2 | 1 | 10
0 | 0 | 1/2 | -3)
Multiply row 3 by 2:
(2 | 0 | -1 | 8
0 | 2 | 1 | 10
0 | 0 | 1 | -6)
Subtract row 3 from row 2:
(2 | 0 | -1 | 8
0 | 2 | 0 | 16
0 | 0 | 1 | -6)
Divide row 2 by 2:
(2 | 0 | -1 | 8
0 | 1 | 0 | 8
0 | 0 | 1 | -6)
Add row 3 to row 1:
(2 | 0 | 0 | 2
0 | 1 | 0 | 8
0 | 0 | 1 | -6)
Divide row 1 by 2:
(1 | 0 | 0 | 1
0 | 1 | 0 | 8
0 | 0 | 1 | -6)
Collect results:
Answer: |x = 1     y = 8      z = -6

Solve the following system:
{x+y = -12
x+z = -11
y+z = -13
Express the system in matrix form:
(1 | 1 | 0
1 | 0 | 1
0 | 1 | 1)(x
y
z) = (-12
-11
-13)
Write the system in augmented matrix form and use Gaussian elimination:
(1 | 1 | 0 | -12
1 | 0 | 1 | -11
0 | 1 | 1 | -13)
Subtract row 1 from row 2:
(1 | 1 | 0 | -12
0 | -1 | 1 | 1
0 | 1 | 1 | -13)
Add row 2 to row 3:
(1 | 1 | 0 | -12
0 | -1 | 1 | 1
0 | 0 | 2 | -12)
Divide row 3 by 2:
(1 | 1 | 0 | -12
0 | -1 | 1 | 1
0 | 0 | 1 | -6)
Subtract row 3 from row 2:
(1 | 1 | 0 | -12
0 | -1 | 0 | 7
0 | 0 | 1 | -6)
Multiply row 2 by -1:
(1 | 1 | 0 | -12
0 | 1 | 0 | -7
0 | 0 | 1 | -6)
Subtract row 2 from row 1:
(1 | 0 | 0 | -5
0 | 1 | 0 | -7
0 | 0 | 1 | -6)
Collect results:
Answer: |x = -5     y = -7     z = -6