Question

Solve the system of equations :

3y - 5z = -23
4x + 2y + 3z = 7
-2x - y - z = -3
a. x = 3, y = 4, z = 2
b. x = -2, y = 1, z = 3
c. x = 1, y = -2, z = 3
d. x = 2, y = 3, z = -4

Answer 1

Upon attempting to solve the system of equations through elimination and substitution, the resulting x value did not match any of the given options. This suggests there might be an error in the provided problem or in the elimination steps used in the calculation.

Step-by-step explanation:

To solve the system of equations, we will use substitution or elimination methods. Here are the given equations:

1. 3y - 5z = -23
2. 4x + 2y + 3z = 7
3. -2x - y - z = -3

Now, let's solve the equations step by step:

1. Let's first isolate y in the third equation:
2. 2x - z = 3 (multiplied by -1)
3. y = 2x - z - 3
4. Now, substitute y in the first and the second equations:
5. 3(2x - z - 3) - 5z = -23
6. 6x - 3z - 9 - 5z = -23
7. 6x - 8z = -14
8. 4x + 2(2x - z - 3) + 3z = 7
9. 4x + 4x - 2z - 6 + 3z = 7
10. 8x + z = 13
11. With these two new equations, we now solve for x and z:
12. 8x + z = 13
13. 6x - 8z = -14 (multiplied by -1):
14. -48x - 8z = 112
15. Add these to eliminate z
16. 8x + z - 48x - 8z = 13 + 112
17. -40x = 125
18. x = 125 / -40
19. x = -3.125 (This is not matching with any of the given options, indicating a possible mistake in the elimination step or in the initial equations provided)

The next step would be solving for y and z using the found x value, but since the x value found does not match any of the provided options, it's possible that there might have been an error either in the elimination process or a transcription error in the given equations, you should double-check the original equations and your steps.