Question

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

Answer 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.