Question

Solve the system of equations 3x - 4y +z=39, -3x + y -2z=-30, 2x -2y + 3z=43

Answer 1

Answer:

x = 2, y = -6, and z = 9

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:

•  3  -4   1      |  39

•  -3   1  -2     |  -30

•  2  -2  3      |  43

Step 2: Add row 1 it into row 2:

•  3 -4   1 |  39

•  0  -3  -1 |   9

•  2 -2  3 |  43

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

•  3 -4   1   |  39

•  0  -3  -1   |   9

•  0  2    7  |  51

Step 4: Multiply row 2 with 2/3 and add it in row 3 and then multiply row 3 with 3:

•  3 -4     1       |  39

•  0 -3    -1       |   9

•  0 0   19/3     |  57

Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• 3x - 4y + z = 39  

• -3y - z = 9

• (19/3)z = 57 (This implies that z = 9.)

Step 6: Since we have calculated z = 9, put this value in equation 2:

• -3y - 9 = 9

• -3y = 18

• y = -6.

Step 8: Put z = 9 and y = -6 in equation 1:

• 3x - 4(-6) + 9 = 39

• 3x + 24 + 9 = 39

• 3x = 6.

• x = 2.

So final answer is x = 2, y = -6, and z = 9!!!