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:

•-8-72|7  

•1-43|-9

•82-5|10

Step 2: Add row 1 it into row 3:

•-8-72|7  

•1-43|-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:

•1-43|-9

•0-3926|-65

•0-5-3|17

Step 4: Divide row 2 with 13:

•1-43|-9

•0-32|-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

•00-19/3|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!!!