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!!!
