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

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!