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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 752 · 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.x + 3y = 15 and 3x + y = 29 →
  2. 2.7x + 9y = 68 and 9x + 7y = 60 →
  3. 3.7x + 4y = 50 and 4x + 7y = 38 →
  4. 4.3x + 8y = 11 and 8x + 3y = 11 →
  5. 5.4x − 4y = 56 and 3x + 3y = 6 →
  6. 6.4x − 6y = 16 and 4x + 6y = −8 →
  7. 7.2x + 4y = 14 and 6x − 6y = 24 →
  8. 8.x − 6y = −3 and 4x − 2y = 10 →
  9. 9.2x + y = 8 and x + 3y = −1 →
  10. 10.6x − 6y = −30 and 2x + 5y = 32 →
  11. 11.5x + 3y = 2 and 2x − 4y = −46 →
  12. 12.5x + y = 34 and x + 5y = 26 →
  13. 13.2x − y = −9 and 5x − 5y = −40 →
  14. 14.2x − 3y = −13 and 6x − 4y = −14 →
  15. 15.6x + 3y = 72 and 3x + 6y = 72 →
  16. 16.3x + 7y = 13 and 7x + 3y = −23 →
  17. 17.6x + 4y = −78 and 3x − 2y = −15 →
  18. 18.2x + 4y = −6 and 2x + 2y = −12 →
  19. 19.2x + y = 0 and x + 2y = 6 →
  20. 20.4x + 2y = −16 and 2x + 4y = −2 →
  21. 21.8x + 2y = 0 and 2x + 8y = 60 →
  22. 22.6x − 3y = 60 and 3x + 5y = 17 →
  23. 23.4x − y = 30 and 4x − 5y = 38 →
  24. 24.3x + y = 5 and 5x − y = −13 →
  25. 25.2x − 5y = −61 and 4x − 5y = −77 →
  26. 26.4x + 7y = 18 and 7x + 4y = −18 →
  27. 27.2x + 2y = 4 and 3x + 6y = −15 →
  28. 28.3x − 2y = 23 and x + 3y = 15 →
  29. 29.7x + 2y = −10 and 2x + 7y = 10 →
  30. 30.3x + 8y = 28 and 8x + 3y = 38 →
  31. 31.4x + 2y = 10 and 6x + 2y = 14 →
  32. 32.4x + 3y = 4 and 2x − y = 22 →
  33. 33.6x + 4y = 74 and 6x − 3y = 39 →
  34. 34.2x + 4y = 26 and 4x + 2y = 22 →
  35. 35.9x + 8y = 121 and 8x + 9y = 117 →
  36. 36.4x − 2y = −4 and 5x + y = −33 →
  37. 37.5x + 6y = −47 and 4x − 3y = 17 →
  38. 38.2x + 4y = 44 and 4x + 2y = 46 →
  39. 39.5x − 3y = 52 and 2x + 2y = −8 →
  40. 40.2x − y = −10 and 4x + y = −8 →

Answer key

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

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