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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 329 · 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 + 6y = −3 and 6x + 5y = 14 →
  2. 2.6x − 2y = −32 and 2x + 2y = 0 →
  3. 3.2x − 2y = −32 and 3x − 4y = −57 →
  4. 4.3x + 4y = 49 and x + 2y = 21 →
  5. 5.7x + 9y = 100 and 9x + 7y = 92 →
  6. 6.6x + 2y = −30 and x + 4y = −16 →
  7. 7.x + 6y = 26 and 6x + y = 16 →
  8. 8.5x + 8y = 7 and 8x + 5y = 19 →
  9. 9.x + 6y = −50 and 4x − 3y = 43 →
  10. 10.6x − y = 52 and 4x + 3y = 42 →
  11. 11.x + 6y = 34 and 2x + 6y = 38 →
  12. 12.6x + 2y = 38 and 5x + y = 31 →
  13. 13.6x + y = 3 and 3x + y = 6 →
  14. 14.3x + 9y = −72 and 9x + 3y = 0 →
  15. 15.2x + 4y = 30 and 2x + y = 6 →
  16. 16.3x + 4y = −12 and 4x + 3y = −23 →
  17. 17.7x + 4y = −24 and 4x + 7y = 24 →
  18. 18.4x + 6y = 48 and 4x + 4y = 36 →
  19. 19.2x − 6y = 8 and x + 3y = −20 →
  20. 20.5x + 3y = −10 and 3x + 5y = 10 →
  21. 21.x + 7y = −4 and 7x + y = 20 →
  22. 22.x + 5y = 28 and 2x − 4y = 0 →
  23. 23.6x + y = 57 and 5x − 3y = 13 →
  24. 24.6x − 5y = 7 and 3x + 4y = 10 →
  25. 25.4x + 2y = 22 and 2x + 4y = 8 →
  26. 26.5x + y = 37 and 6x + 5y = 71 →
  27. 27.x − 6y = −15 and x − 2y = −11 →
  28. 28.4x + 6y = 78 and x − 2y = −5 →
  29. 29.x + 5y = −7 and 2x + 6y = −2 →
  30. 30.x + 9y = −48 and 9x + y = 48 →
  31. 31.6x + 4y = 6 and 6x + 2y = 12 →
  32. 32.5x + 8y = 19 and 8x + 5y = −32 →
  33. 33.5x + 6y = 64 and 3x + y = 28 →
  34. 34.9x + 8y = 81 and 8x + 9y = 89 →
  35. 35.4x + 2y = 36 and 2x + 4y = 42 →
  36. 36.4x − 4y = 56 and 3x − 6y = 69 →
  37. 37.5x + 9y = 50 and 9x + 5y = 34 →
  38. 38.3x + 7y = 34 and 7x + 3y = −14 →
  39. 39.3x − y = 16 and x + 6y = 56 →
  40. 40.x + y = 15 and 5x + 6y = 84 →

Answer key

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

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