Answer:
x = -1, y = -1, and z = -4.
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!!!