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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 595 · 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 + 5y = 13 and 5x + y = 41 →
  2. 2.4x + 9y = 15 and 9x + 4y = −15 →
  3. 3.6x + 7y = −4 and 7x + 6y = −9 →
  4. 4.x − 4y = 39 and 3x − 2y = 27 →
  5. 5.3x − 3y = −15 and 3x + 3y = 3 →
  6. 6.x − 2y = 0 and 6x + y = 39 →
  7. 7.2x − 6y = −52 and 2x + 4y = 18 →
  8. 8.5x + 2y = 40 and 2x + 5y = 37 →
  9. 9.6x − 4y = 48 and 5x + 6y = −16 →
  10. 10.3x + 4y = 35 and 5x + 2y = 49 →
  11. 11.5x + y = 39 and 5x − 6y = −24 →
  12. 12.5x − y = 0 and 4x + 6y = 34 →
  13. 13.5x + 3y = 52 and 6x + 2y = 56 →
  14. 14.2x − 3y = −5 and 6x + 2y = −48 →
  15. 15.9x + 8y = 82 and 8x + 9y = 88 →
  16. 16.4x − 5y = −21 and x + 5y = 26 →
  17. 17.5x − 2y = 6 and x + 4y = −34 →
  18. 18.6x + 5y = −49 and 3x + 4y = −23 →
  19. 19.5x + 8y = 26 and 8x + 5y = 26 →
  20. 20.5x + 4y = −1 and 4x + 5y = −17 →
  21. 21.5x + 3y = 39 and 3x + 5y = 49 →
  22. 22.6x + 3y = 51 and 3x + 6y = 30 →
  23. 23.x + 5y = 34 and 6x + 5y = 79 →
  24. 24.7x + 4y = 42 and 4x + 7y = 57 →
  25. 25.4x − 3y = −30 and 6x + 5y = −26 →
  26. 26.x + 3y = 14 and 3x + y = −14 →
  27. 27.x − 4y = −16 and 3x + 6y = 42 →
  28. 28.6x + 7y = −25 and 7x + 6y = −14 →
  29. 29.6x − 3y = 51 and 6x + y = 23 →
  30. 30.4x + 7y = 55 and 7x + 4y = 55 →
  31. 31.8x + 9y = 112 and 9x + 8y = 109 →
  32. 32.5x + 4y = −46 and 4x + 5y = −53 →
  33. 33.5x + y = −15 and 4x + y = −11 →
  34. 34.5x + y = 2 and 5x + 6y = 37 →
  35. 35.2x + 3y = 15 and 2x − 5y = −41 →
  36. 36.2x + 6y = −10 and 6x + 2y = −46 →
  37. 37.5x + 3y = −66 and 4x + 2y = −50 →
  38. 38.4x − y = 19 and 2x + 5y = 37 →
  39. 39.6x − 5y = −66 and x + 4y = 18 →
  40. 40.5x + 4y = −2 and 2x + 5y = 6 →

Answer key

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

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