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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 495 · 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. 1.2x + 5y = 1 and 4x − 4y = −12 →
  2. 2.3x + 4y = 25 and 4x + 3y = 24 →
  3. 3.6x + 5y = 9 and 5x − 2y = −48 →
  4. 4.9x + 8y = −17 and 8x + 9y = 0 →
  5. 5.8x + 7y = 72 and 7x + 8y = 78 →
  6. 6.7x + 3y = 78 and 3x + 7y = 62 →
  7. 7.4x + 5y = 13 and 5x + 4y = 14 →
  8. 8.9x + 8y = 71 and 8x + 9y = 65 →
  9. 9.x + 4y = 41 and 5x + 5y = 85 →
  10. 10.5x + 6y = 31 and 6x + 5y = 35 →
  11. 11.4x + 9y = −76 and 9x + 4y = −41 →
  12. 12.5x + 2y = 59 and x + 5y = 44 →
  13. 13.5x + 6y = 41 and 6x − 6y = −30 →
  14. 14.8x + 2y = −58 and 2x + 8y = −22 →
  15. 15.2x + 5y = −32 and 5x + 2y = −17 →
  16. 16.5x − 3y = 44 and x + 6y = −11 →
  17. 17.3x + 6y = 12 and 6x + 6y = −6 →
  18. 18.5x − 2y = 39 and x + 6y = −5 →
  19. 19.5x + 2y = 23 and 3x + 2y = 17 →
  20. 20.2x + 6y = −40 and 2x + 4y = −22 →
  21. 21.3x + 2y = −15 and 2x + 3y = −15 →
  22. 22.2x + 3y = −3 and 6x + 6y = 12 →
  23. 23.x + 8y = 54 and 8x + y = 54 →
  24. 24.2x + 2y = −22 and 5x − 5y = 35 →
  25. 25.3x − 5y = 19 and 3x + 2y = −16 →
  26. 26.2x + y = 7 and 2x + 2y = 2 →
  27. 27.2x + 6y = 60 and 6x + 2y = 68 →
  28. 28.6x − 4y = 12 and 2x + 6y = 26 →
  29. 29.6x + 5y = −9 and 5x + 6y = −13 →
  30. 30.x + y = 5 and 6x − 6y = 54 →
  31. 31.5x + y = 34 and 5x + 2y = 43 →
  32. 32.6x + 5y = −59 and 5x + 6y = −62 →
  33. 33.6x + y = 31 and 5x − 2y = 6 →
  34. 34.8x + y = −46 and x + 8y = −53 →
  35. 35.4x + 6y = −12 and 4x − y = 44 →
  36. 36.3x + 2y = 20 and 3x + 4y = 34 →
  37. 37.x − 2y = 0 and 4x + 5y = 13 →
  38. 38.6x + 5y = 78 and 3x − 5y = −6 →
  39. 39.3x + 6y = −57 and 4x + 3y = −51 →
  40. 40.3x − 2y = 5 and 4x − y = 10 →

Answer key

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

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