What is the solution to the following system?

-4y=8

x+3y-3z=-26

2x-5y+z=19

a) x = - 53, y = - 2, z = 7

b) x = - 41, y = - 2, z = - 7

c) x = - 11, y = - 2, z = - 7

d) x = 1, y = - 2, z = 7

Option D (x = 1, y = - 2, and z = 7).

Step-by-step explanation:

This question can be solved using multiple ways. I will use the Gauss Jordan Method.

Step 1: Convert the system into the augmented matrix form:

• 0 - 4 0 | 8

• 1 3 - 3 | - 26

• 2 - 5 1 | 19

Step 2: Divide row 1 by - 4 and switch row 1 and row 2:

• 1 3 - 3 | - 26

• 0 1 0 | - 2

• 2 - 5 1 | 19

Step 3: Multiply row 1 with - 2 and add it in row 3:

• 1 3 - 3 | - 26

• 0 1 0 | - 2

• 0 - 11 7 | 71

Step 4: Multiply row 2 with 11 and add it in row 3:

• 1 3 - 3 | - 26

• 0 1 0 | - 2

• 0 0 7 | 49

Step 5: Divide row 3 with 7:

• 1 3 - 3 | - 26

• 0 1 0 | - 2

• 0 0 1 | 7

Step 6: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• x + 3y - 3z = - 26

• y = - 2

• z = 7

Step 7: Put z = 7 and y = - 2 in equation 1:

• x + 3 (-2) - 3 (7) = - 26

• x - 6 - 21 = - 26

• x = 1.

So final answer is x = 1, y = - 2, and z = 7. Therefore, Option D is the correct answer!