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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 526 · 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 = 24 and 3x + 5y = 28 →
  2. 2.5x + 2y = −24 and 6x + 6y = −54 →
  3. 3.x − 4y = 26 and 5x − 6y = 46 →
  4. 4.5x − 2y = 51 and 3x − 6y = 69 →
  5. 5.2x + 6y = −40 and 5x − 2y = 19 →
  6. 6.5x − 4y = 4 and x + 6y = 28 →
  7. 7.3x + 4y = 31 and 4x − 2y = −10 →
  8. 8.4x + 6y = 38 and x + 2y = 11 →
  9. 9.x − y = −16 and x + 4y = 19 →
  10. 10.8x + 9y = 55 and 9x + 8y = 64 →
  11. 11.4x − 6y = 72 and x + 2y = −3 →
  12. 12.6x + 3y = −6 and 5x + 3y = −8 →
  13. 13.6x + 3y = −24 and 5x + 2y = −23 →
  14. 14.9x + 3y = −6 and 3x + 9y = 30 →
  15. 15.2x + 2y = −6 and 3x − 2y = 31 →
  16. 16.5x − y = 47 and 2x + 6y = 6 →
  17. 17.3x − 6y = 0 and 4x + 5y = 13 →
  18. 18.4x + y = 24 and x − y = 1 →
  19. 19.5x − 6y = 35 and x + 5y = −24 →
  20. 20.4x + 6y = 52 and 6x + 4y = 38 →
  21. 21.x + 6y = −24 and 5x + 6y = −48 →
  22. 22.6x − 5y = 70 and 5x + y = 17 →
  23. 23.3x − 2y = 24 and 6x + 4y = 0 →
  24. 24.5x − 2y = −28 and 2x + 3y = −15 →
  25. 25.6x + 6y = 24 and 6x + 5y = 16 →
  26. 26.8x + 9y = 153 and 9x + 8y = 153 →
  27. 27.2x + 4y = −2 and 5x + 5y = 5 →
  28. 28.x − y = 2 and 2x + 6y = 20 →
  29. 29.5x + 6y = 37 and 3x + 4y = 25 →
  30. 30.2x + 4y = 28 and 3x + 5y = 39 →
  31. 31.8x + y = 35 and x + 8y = 28 →
  32. 32.3x + 9y = −57 and 9x + 3y = −3 →
  33. 33.2x + 4y = 18 and 2x − 3y = −10 →
  34. 34.x + 4y = 22 and 3x + y = 11 →
  35. 35.4x + 4y = 44 and x − 6y = −38 →
  36. 36.6x + y = 51 and x + 6y = 26 →
  37. 37.2x + 8y = −70 and 8x + 2y = −10 →
  38. 38.3x − 5y = −20 and 2x + 5y = −5 →
  39. 39.5x + 9y = 38 and 9x + 5y = 46 →
  40. 40.x − 2y = −5 and 4x + 5y = 71 →

Answer key

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

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