Question

What is the solution to the following system?

Answer 1

Answer:

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!!!