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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 396 · 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. 1.9x + y = 48 and x + 9y = 32 →
  2. 2.2x + 6y = −18 and 4x + 5y = −1 →
  3. 3.5x − 3y = 18 and 4x + 5y = 81 →
  4. 4.4x + 6y = −34 and 5x − 5y = −30 →
  5. 5.2x + 6y = 24 and 6x + 2y = 56 →
  6. 6.6x + 6y = 60 and x + 2y = 13 →
  7. 7.3x − 5y = 10 and 4x − 3y = 17 →
  8. 8.6x − 2y = 50 and x − y = 7 →
  9. 9.4x + 4y = 16 and x − y = 2 →
  10. 10.8x + 5y = 61 and 5x + 8y = 82 →
  11. 11.3x + 5y = 17 and 5x − y = 19 →
  12. 12.x + 6y = 4 and 6x + y = −46 →
  13. 13.2x + 3y = 39 and 3x + 2y = 36 →
  14. 14.3x + 2y = −6 and 5x + 3y = −11 →
  15. 15.3x − 6y = −54 and x − 5y = −36 →
  16. 16.x + 8y = 23 and 8x + y = 58 →
  17. 17.2x − 3y = 4 and 4x + 3y = 44 →
  18. 18.x − y = 8 and 3x + 6y = 33 →
  19. 19.x + 2y = 1 and 3x − y = 10 →
  20. 20.x − 4y = 15 and 2x + 6y = −12 →
  21. 21.5x + 3y = −2 and 3x + 5y = 2 →
  22. 22.9x + 8y = −29 and 8x + 9y = −39 →
  23. 23.x − 2y = 15 and 2x + y = 15 →
  24. 24.8x + 2y = 46 and 2x + 8y = 64 →
  25. 25.x + 3y = 27 and 4x − 3y = 3 →
  26. 26.4x − y = 25 and 2x − 2y = 8 →
  27. 27.6x + 2y = 14 and 2x + 6y = −38 →
  28. 28.3x − 4y = −27 and 5x − 4y = −37 →
  29. 29.7x + 6y = 91 and 6x + 7y = 91 →
  30. 30.x + 6y = 12 and 4x − 5y = 19 →
  31. 31.3x − 3y = −27 and 4x + 6y = 44 →
  32. 32.2x + 6y = 28 and 5x + y = 42 →
  33. 33.3x − y = 24 and 3x + 3y = 36 →
  34. 34.2x + 9y = 24 and 9x + 2y = −46 →
  35. 35.4x − 4y = 4 and 5x + y = 17 →
  36. 36.4x + 5y = 13 and x + y = 4 →
  37. 37.8x + 9y = 113 and 9x + 8y = 108 →
  38. 38.5x + 4y = 14 and 2x + 3y = 7 →
  39. 39.4x − 2y = −52 and 2x + 2y = −2 →
  40. 40.4x + 3y = 1 and x + 3y = −2 →

Answer key

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

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