Solve the system of equations. 5x+9y+9z=5 4x+9y+6z=10 2x+2y+5z=9 Answer choices:

a. x=116, y=8, z=-21

b. x=82, y=-10, z=9

c. x=-116, y=28, z=37

d. x=6, y=-14, z=1

5x + 9y + 9z = 5 ⇒ 5x + 9y + 9z = 5

4x + 9y + 6z = 10 ⇒ 4x + 9y + 6z = 10

2x + 2y + 5z = 9 9x + 18y + 15z = 15

5x + 9y + 9z = 5 ⇒ 4x + 9y + 6z = 10

4x + 9y + 6z = 10 ⇒ 2x + 2y + 5z = 9

2x + 2y + 5z = 9 6x + 11y + 11z = 19

9x + 18y + 15z = 15 ⇒ 99x + 198y + 165z = 165

6x + 11y + 11z = 19 ⇒ 90x + 165y + 165z = 285

9x + 33y = - 120

5x + 9y + 9z = 5 ⇒ 5x + 9y + 9z = 5

4x + 9y + 6z = 10 ⇒ 4x + 9y + 6z = 10

2x + 2y + 5z = 9 ⇒ 1x + 0y + 3z = - 5

5x + 9y + 9z = 5 ⇒ 4x + 9y + 6z = 10

4x + 9y + 6z = 10 ⇒ 2x + 2y + 5z = 9

2x + 2y + 5z = 9 2x + 7y + 1z = 1

1x + 0y + 3z = - 5 ⇒ 1x + 0y + 3z = - 5

2x + 7y + 1z = 1 ⇒ 6x + 21y + 3z = 3

-5x - 21y = - 8

9x + 33y = - 120 ⇒ 63x + 231y = - 840

-5x - 21y = - 8 ⇒ - 55x - 231y = - 88

8x = - 928

8 8

x = - 116

-5x - 21y = - 8

-5 (-116) - 21y = - 8

580 - 21y = - 8

- 580 - 580

-21y = - 588

-21 - 21

y = 28

5x + 9y + 9z = 5

5 (-116) + 9 (28) + 9z = 5

-580 + 252 + 9z = 5

-328 + 9z = 5

+ 328 + 328

9z = 333

9 9

z = 37

(x, y, z) = (-116, 28, 37)

The answer to the problem is C.