Which of the following is a solution to the system?

x = -2 , y = 3 , z = -5 thus the answer is C.)

Step-by-step explanation:

Solve the following system:

{3 x + 2 y - 3 z = 15

-2 x + 4 y + 2 z = 6

4 z + 12 = -8

Express the system in standard form:

{3 x + 2 y - 3 z = 15

-2 x + 4 y + 2 z = 6

0 + 0 + 4 z = -20

Express the system in matrix form:

(3 | 2 | -3

-2 | 4 | 2

0 | 0 | 4)(x

y

z) = (15

6

-20)

Write the system in augmented matrix form and use Gaussian elimination:

(3 | 2 | -3 | 15

-2 | 4 | 2 | 6

0 | 0 | 4 | -20)

Add 2/3 × (row 1) to row 2:

(3 | 2 | -3 | 15

0 | 16/3 | 0 | 16

0 | 0 | 4 | -20)

Multiply row 2 by 3/16:

(3 | 2 | -3 | 15

0 | 1 | 0 | 3

0 | 0 | 4 | -20)

Divide row 3 by 4:

(3 | 2 | -3 | 15

0 | 1 | 0 | 3

0 | 0 | 1 | -5)

Subtract 2 × (row 2) from row 1:

(3 | 0 | -3 | 9

0 | 1 | 0 | 3

0 | 0 | 1 | -5)

Add 3 × (row 3) to row 1:

(3 | 0 | 0 | -6

0 | 1 | 0 | 3

0 | 0 | 1 | -5)

Divide row 1 by 3:

(1 | 0 | 0 | -2

0 | 1 | 0 | 3

0 | 0 | 1 | -5)

Collect results:

 {x = -2 , y = 3 , z = -5

the answers c