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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 931 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.3x + 6y = −33 and 6x + 2y = 14 →
  2. 2.5x − 6y = 63 and 5x − 3y = 54 →
  3. 3.3x + 5y = 24 and 5x + y = −4 →
  4. 4.4x − 3y = 2 and 5x − 5y = 5 →
  5. 5.x + 3y = 23 and 3x + y = 13 →
  6. 6.7x + 2y = 9 and 2x + 7y = 9 →
  7. 7.3x + 5y = 64 and 5x + 3y = 64 →
  8. 8.8x + 5y = 99 and 5x + 8y = 96 →
  9. 9.5x − 4y = 6 and 2x + 3y = 30 →
  10. 10.3x − 4y = 0 and 4x + y = −19 →
  11. 11.6x + 3y = 45 and 3x + 2y = 24 →
  12. 12.9x + y = 70 and x + 9y = 70 →
  13. 13.5x + y = 19 and x + 5y = −1 →
  14. 14.2x − 6y = 32 and 5x + 2y = −5 →
  15. 15.5x + 2y = 2 and 5x − y = 14 →
  16. 16.5x + y = 24 and 4x − y = 3 →
  17. 17.2x + 3y = 28 and 6x + 3y = 60 →
  18. 18.2x + 3y = −16 and 3x + 2y = −14 →
  19. 19.4x − 4y = 8 and x − 4y = −1 →
  20. 20.2x + 4y = 22 and 4x + 4y = 28 →
  21. 21.2x + 6y = −56 and 3x + 2y = −28 →
  22. 22.6x + 3y = 39 and 2x + 6y = −12 →
  23. 23.6x + 3y = −30 and 5x + 6y = −11 →
  24. 24.3x + 2y = 10 and 5x − 3y = 4 →
  25. 25.3x − 3y = −3 and 3x − 5y = −7 →
  26. 26.9x + 6y = −117 and 6x + 9y = −108 →
  27. 27.9x + 8y = 121 and 8x + 9y = 117 →
  28. 28.6x + y = −59 and 2x + y = −23 →
  29. 29.3x − 4y = 23 and 5x − 4y = 41 →
  30. 30.x + 5y = 20 and 3x + 4y = 5 →
  31. 31.x + 4y = 19 and 4x + y = 1 →
  32. 32.6x + 3y = 51 and 6x − y = 31 →
  33. 33.2x + y = −8 and x + 3y = 6 →
  34. 34.x + 8y = −37 and 8x + y = 19 →
  35. 35.x + 5y = 10 and 5x + 2y = −19 →
  36. 36.x + 3y = 12 and 3x + y = 20 →
  37. 37.2x + 8y = −32 and 8x + 2y = 52 →
  38. 38.3x + 2y = 42 and x − y = −1 →
  39. 39.x + 3y = 13 and 6x − 5y = −14 →
  40. 40.2x − y = 1 and 5x + y = 6 →

Answer key

  1. x = 5, y = −8
  2. x = 9, y = −3
  3. x = −2, y = 6
  4. x = −1, y = −2
  5. x = 2, y = 7
  6. x = 1, y = 1
  7. x = 8, y = 8
  8. x = 8, y = 7
  9. x = 6, y = 6
  10. x = −4, y = −3
  11. x = 6, y = 3
  12. x = 7, y = 7
  13. x = 4, y = −1
  14. x = 1, y = −5
  15. x = 2, y = −4
  16. x = 3, y = 9
  17. x = 8, y = 4
  18. x = −2, y = −4
  19. x = 3, y = 1
  20. x = 3, y = 4
  21. x = −4, y = −8
  22. x = 9, y = −5
  23. x = −7, y = 4
  24. x = 2, y = 2
  25. x = 1, y = 2
  26. x = −9, y = −6
  27. x = 9, y = 5
  28. x = −9, y = −5
  29. x = 9, y = 1
  30. x = −5, y = 5
  31. x = −1, y = 5
  32. x = 6, y = 5
  33. x = −6, y = 4
  34. x = 3, y = −5
  35. x = −5, y = 3
  36. x = 6, y = 2
  37. x = 8, y = −6
  38. x = 8, y = 9
  39. x = 1, y = 4
  40. x = 1, y = 1

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