I kept the variables to minimum in order to avoid having to compute very large numbers that may distract the students from understanding the methods involved in solving this particular type of algebraic problem.
| 1. | 3x - 5y + 4z = 23 and x - 2y + 2z = 9 and 5x - 6y - 3z = 14 |
| Answer: x = 7; y = 2; z = 3 | |
| 2. | 5x + 2y - 5z = 0 and 6x + y - 2z = 9 and 5x - 4y - 5z = -30 |
| Answer: x = 2; y = 5; z = 4 | |
| 3. | 5x - y - z = 14 and 5x - 2y - 3z = 7 and 3x - 2y + 3z = 5 |
| Answer: x = 4; y = 5; z = 1 | |
| 4. | 4x - 3y + 2z = -1 and 3x + y - 3z = 4 and 6x - y - 4z = -5 |
| Answer: x = 3; y = 7; z = 4 | |
| 5. | 3x + 6y + z = 11 and 2x - 5y - 5z = -13 and x + 4y + 3z = 11 |
| Answer: x = 1; y = 1; z = 2 | |
| 6. | 3x + y + 2z = 1 and 3x - y + 6z = -1 and 3x - 2y + 3z = 13 |
| Answer: x = 4; y = -5; z = -3 | |
| 7. | 5x - 2y - 2z = -8 and x + 6y - z = 0 and 5x + 4y + 2z = 30 |
| Answer: x = 2; y = 1; z = 8 | |
| 8. | 4x - 3y + z = -14 and 6x + y + 4z = 3 and 2x + 3y + 4z = 17 |
| Answer: x = -2; y = 3; z = 3 | |
| 9. | 3x - y - z = -9 and 2x + y + z = -1 and x - 5y - 3z = -9 |
| Answer: x = -2; y = -1; z = 4 | |
| 10. | 2x - y - 3z = -11 and x + 3y + z = 14 and x - 3y - 2z = -13 |
| Answer: x = 3; y = 2; z = 5 | |
| 11. | 3x + 4y + 4z = 34 and 2x - 3y + 2z = 15 and 2x + y - 3z = 4 |
| Answer: x = 6; y = 1; z = 3 | |
| 12. | 3x - y + 4z = 6 and x + 3y + z = 15 and 3x - 4y - 3z = -13 |
| Answer: x = 2; y = 4; z = 1 | |
| 13. | 3x + 3y + 2z = -8 and 3x - 2y - 5z = -8 and 5x + 4y + z = -18 |
| Answer: x = 1; y = -7; z = 5 | |
| 14. | x - y + 4z = 4 and 5x + y + 3z = -11 and 5x + 3y + z = -3 |
| Answer: x = -7; y = 9; z = 5 | |
| 15. | 3x - 2y + 3z = -15 and 5x + 4y + z = -11 and x + 5y + 3z = 16 |
| Answer: x = -5; y = 3; z = 2 | |
| 16. | 3x + 5y - 2z = 14 and 5x + 3y - 4z = 16 and 3x - 4y + 3z = 20 |
| Answer: x = 5; y = 1; z = 3 | |
| 17. | 6x + y + 3z = -6 and 7x - 4y + 5z = -2 and x - 6y + 5z = -14 |
| Answer: x = 3; y = -3; z = -7 | |
| 18. | 6x - y - 6z = 23 and 5x - 4y + z = -20 and x - 6y - 5z = 22 |
| Answer: x = -2; y = 1; z = -6 | |
| 19. | 5x + 3y - 2z = 15 and 3x + 2y + 3z = 27 and 3x + 5y - 5z = 13 |
| Answer: x = 1; y = 6; z = 4 | |
| 20. | 4x - 3y + 2z = -2 and 3x - y + 3z = 8 and 6x - y + 4z = 14 |
| Answer: x = 1; y = 4; z = 3 | |
| 21. | x - y - 4z = -22 and 5x - y - 3z = 11 and 5x - 3y - z = 3 |
| Answer: x = 7; y = 9; z = 5 | |
| 22. | 4x - 3y + 2z = 11 and 2x + 3y + z = 10 and 4x + 3y + 4z = 23 |
| Answer: x = 2; y = 1; z = 3 | |
| 23. | 4x + 3y + 2z = 27 and x + 2y + 3z = 13 and 2x + 3y + z = 18 |
| Answer: x = 4; y = 3; z = 1 | |
| 24. | x - 3y - 4z = -33 and x + y - 5z = -38 and x - 5y - z = -8 |
| Answer: x = 6; y = 1; z = 9 | |
| 25. | 5x - 3y + 5z = -15 and 3x + y + 5z = -1 and 3x - y - 5z = 19 |
| Answer: x = 3; y = 5; z = -3 | |
| 26. | x - y - 7z = -8 and 9x - 4y - 5z = 11 and 5x - y + 3z = 18 |
| Answer: x = 4; y = 5; z = 1 | |
| 27. | 2x - y - 5z = -13 and 2x - 3y - 5z = -17 and x - 2y - 2z = -8 |
| Answer: x = 2; y = 2; z = 3 | |
| 28. | x - 3y + 3z = 3 and 2x + y + 2z = 9 and x - y + 2z = 4 |
| Answer: x = 3; y = 1; z = 1 | |
| 29. | x - 3y + 6z = 25 and x - 4y + 9z = 38 and x - y + 5z = 24 |
| Answer: x = 1; y = 2; z = 5 | |
| 30. | x - 3y + z = -10 and 3x + 3y - 4z = 21 and 2x - y - 3z = -5 |
| Answer: x = 5; y = 6; z = 3 | |
