Solve the system algebraically.

x − y + 2z = -3

2x + 2y − z = -3

3x + 2y = 8

no solution

(-42, 67, 53)

infinite solutions

(43, -57, 63)

1x -  1y + 2z = -3 → 1x -  1y + 2z = -3 → 2x -  2y + 4z = -6
2x + 2y -  1z = -3 → 2x + 2y -  1z = -3 → 2x + 2y -  1z = -3
3x + 2y + 0z =  8                                               4x + 3z = -9
 
1x -  1y + 2z = -3
2x + 2y -  1z = -3 → 2x + 2y -  1z = -3 → -2x - 2y + 1z = 3
3x + 2y + 0z =  8 → 3x + 2y +  0z =  8 → 3x + 2y + 0z = 8
                                                                              x + z = 11

4x + 3z = -9 →  4x + 3z = -9
1x + 1z = 11 → 4x + 4z = 44
                                  -z = -53
                                  -1     -1
                                   z = 53
x +   z = 11
x + 53 = 11
    - 53  - 53
        x = -42

      3x + 2y = 8
3(-42) + 2y = 8
  -126 + 2y = 8
+ 126     + 126
             2y = 134
              2        2
               y = 67
     (x, y, z) = (-42, 67, 53)

The answer is B.

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