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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 84 · 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. 1.4x + 4y = 8 and x − 5y = 38 →
  2. 2.4x + 2y = −26 and 2x + 4y = −10 →
  3. 3.6x + 6y = −12 and 5x − 2y = 32 →
  4. 4.x + y = 5 and 6x + 4y = 26 →
  5. 5.6x + 5y = 7 and 5x + 4y = 7 →
  6. 6.4x + 4y = 44 and x − y = −7 →
  7. 7.2x + 4y = −20 and x − 5y = 39 →
  8. 8.x + y = −6 and x − y = 12 →
  9. 9.5x + 2y = 17 and 2x + 5y = 11 →
  10. 10.3x − 2y = 3 and x − 5y = −25 →
  11. 11.4x − y = −31 and 3x − 4y = −46 →
  12. 12.3x + 5y = 51 and 4x + y = 17 →
  13. 13.5x + 3y = 67 and 4x + 4y = 68 →
  14. 14.6x + 3y = 69 and 6x + 5y = 87 →
  15. 15.x + 9y = 82 and 9x + y = 18 →
  16. 16.8x + 7y = 18 and 7x + 8y = 27 →
  17. 17.2x + 9y = −29 and 9x + 2y = 62 →
  18. 18.8x + 6y = −34 and 6x + 8y = −8 →
  19. 19.2x + 3y = 37 and x + 3y = 32 →
  20. 20.x + 3y = −17 and 5x − 3y = 41 →
  21. 21.3x − 4y = 11 and x + 2y = 7 →
  22. 22.6x + 3y = −9 and 3x + 6y = 18 →
  23. 23.2x − y = 0 and 4x + 3y = −30 →
  24. 24.x + 5y = −2 and 6x + y = 17 →
  25. 25.2x + 9y = −11 and 9x + 2y = 66 →
  26. 26.4x + 2y = 44 and 3x + 3y = 39 →
  27. 27.3x + y = 36 and 6x − y = 45 →
  28. 28.6x − 3y = −45 and 6x + 6y = −36 →
  29. 29.4x − y = −2 and 5x + 5y = −15 →
  30. 30.6x + 5y = 82 and 2x + 6y = 62 →
  31. 31.3x + 6y = −15 and 4x + 2y = 4 →
  32. 32.3x + 2y = 5 and 2x + 3y = 5 →
  33. 33.3x + y = −13 and 2x − 6y = 38 →
  34. 34.5x − 4y = 9 and 5x + 4y = 81 →
  35. 35.x + 8y = 52 and 8x + y = −25 →
  36. 36.3x + 5y = 31 and 5x + 3y = 25 →
  37. 37.9x + 2y = −62 and 2x + 9y = 29 →
  38. 38.3x − y = −8 and 5x + 5y = 20 →
  39. 39.2x + 6y = 64 and 2x − 6y = −32 →
  40. 40.5x + 2y = 29 and 2x + 5y = 20 →

Answer key

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

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