Solve the system of equations.

-8x - 7y + 2z = 7

x - 4y + 3z = - 9

8x + 2y - 5z = 10

x = - 1, y = - 1, and z = - 4.

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:

• - 8 - 7 2 | 7

• 1 - 4 3 | - 9

• 8 2 - 5 | 10

Step 2: Add row 1 it into row 3:

• - 8 - 7 2 | 7

• 1 - 4 3 | - 9

• 0 - 5 - 3 | 17

Step 3: Multiply row 2 with 8 and add it in row 1 and interchange row 2 and row 1:

• 1 - 4 3 | - 9

• 0 - 39 26 | - 65

• 0 - 5 - 3 | 17

Step 4: Divide row 2 with 13:

• 1 - 4 3 | - 9

• 0 - 3 2 | - 5

• 0 - 5 - 3 | 17

Step 5: Multiply row 2 with - 5/3 and add it in row 3:

• 1 - 4 3 | - 9

• 0 - 3 2 | - 5

• 0 0 - 19/3 | 76/3

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

• x - 4y + 3z = - 9

• - 3y + 2z = - 5

• (-19/3) z = 76/3 (This implies that z = - 4.)

Step 7: Since we have calculated z = - 4, put this value in equation 2:

• - 3y + 2 (-4) = - 5

• - 3y = 3

• y = - 1.

Step 8: Put z = - 4 and y = - 1 in equation 1:

• x - 4 (-1) + 3 (-4) = - 9

• x + 4 - 12 = - 9

• x = - 1.

So final answer is x = - 1, y = - 1, and z = - 4!