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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 131 · 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. 1.5x + 4y = 60 and 4x + 5y = 57 →
  2. 2.3x + 5y = −3 and 6x − y = 27 →
  3. 3.4x − 5y = 31 and 2x + 2y = 2 →
  4. 4.3x + y = 31 and x + 3y = 21 →
  5. 5.4x + 4y = −32 and 6x + 2y = −52 →
  6. 6.6x + 9y = 93 and 9x + 6y = 87 →
  7. 7.3x + 5y = −33 and x + 2y = −12 →
  8. 8.6x + 7y = 33 and 7x + 6y = 45 →
  9. 9.7x + 4y = −50 and 4x + 7y = −71 →
  10. 10.7x + 4y = 23 and 4x + 7y = 32 →
  11. 11.x + 8y = 49 and 8x + y = 77 →
  12. 12.5x + 6y = 83 and 6x + 5y = 82 →
  13. 13.3x + 9y = 48 and 9x + 3y = 24 →
  14. 14.3x + 4y = −5 and 4x + 3y = −9 →
  15. 15.9x + 8y = 103 and 8x + 9y = 101 →
  16. 16.6x − y = −7 and 6x + 4y = −2 →
  17. 17.5x + 3y = 37 and 3x + 5y = 35 →
  18. 18.8x + 6y = 86 and 6x + 8y = 82 →
  19. 19.2x + 9y = 46 and 9x + 2y = −24 →
  20. 20.x + 3y = 13 and 4x + 5y = 24 →
  21. 21.6x + 3y = −75 and 2x + 4y = −52 →
  22. 22.3x + 5y = −13 and 5x + 5y = −15 →
  23. 23.3x − 6y = −30 and 2x + 2y = 16 →
  24. 24.3x + 2y = 13 and 2x + 3y = 17 →
  25. 25.x + y = 10 and 6x + 5y = 56 →
  26. 26.x + 5y = 24 and 5x + 3y = 54 →
  27. 27.3x + 6y = −6 and 5x + 4y = −16 →
  28. 28.7x + 4y = −31 and 4x + 7y = 20 →
  29. 29.2x + 2y = −10 and 5x − 3y = 7 →
  30. 30.x + 9y = −43 and 9x + y = 13 →
  31. 31.6x + 4y = 68 and 4x + 6y = 72 →
  32. 32.2x − 6y = −34 and 6x + 3y = −39 →
  33. 33.3x + 4y = −46 and 5x + 2y = −44 →
  34. 34.x + 5y = 42 and 4x + 5y = 48 →
  35. 35.3x + y = 29 and 2x − 5y = 8 →
  36. 36.4x + 7y = 39 and 7x + 4y = 60 →
  37. 37.6x + 2y = 24 and x + 5y = 32 →
  38. 38.5x + 3y = 22 and 6x + 5y = 25 →
  39. 39.6x + 5y = 24 and x − 2y = −13 →
  40. 40.3x + 2y = 25 and 2x + y = 14 →

Answer key

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

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