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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 892 · 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 + 2y = 7 and 4x − 6y = −70 →
  2. 2.5x + 2y = −10 and 6x − 3y = −39 →
  3. 3.6x + 5y = 61 and x − y = 1 →
  4. 4.6x − 4y = −62 and x − 2y = −13 →
  5. 5.5x − 5y = −45 and x + 3y = 23 →
  6. 6.9x + 7y = 135 and 7x + 9y = 137 →
  7. 7.6x + 7y = 13 and 7x + 6y = 13 →
  8. 8.4x + 8y = −16 and 8x + 4y = 16 →
  9. 9.7x + y = 47 and x + 7y = 41 →
  10. 10.2x − y = 10 and 4x + 5y = 62 →
  11. 11.x + 8y = −64 and 8x + y = 55 →
  12. 12.8x + 6y = 26 and 6x + 8y = 30 →
  13. 13.4x + y = 29 and x + 4y = 26 →
  14. 14.6x − 5y = 82 and 6x + y = 34 →
  15. 15.5x + 6y = 53 and 3x − 2y = 15 →
  16. 16.6x + y = −9 and x + 6y = 51 →
  17. 17.x + 9y = 25 and 9x + y = 65 →
  18. 18.x + 7y = −28 and 7x + y = 44 →
  19. 19.x + 2y = −18 and 2x + y = −15 →
  20. 20.2x + 3y = 19 and 2x + y = 17 →
  21. 21.3x + y = −16 and x + 3y = 8 →
  22. 22.4x − 4y = −48 and 4x + 3y = −13 →
  23. 23.4x + 5y = 8 and 5x + 4y = −8 →
  24. 24.3x − 3y = −9 and 4x + 3y = −47 →
  25. 25.5x + 5y = 65 and 4x + 3y = 48 →
  26. 26.9x + 7y = 41 and 7x + 9y = 39 →
  27. 27.4x + 6y = −20 and 6x + 4y = 0 →
  28. 28.x − 3y = −29 and 4x + 4y = −4 →
  29. 29.5x − 5y = −5 and 3x + 5y = 61 →
  30. 30.2x + y = −4 and 5x + 4y = −22 →
  31. 31.x + 9y = 34 and 9x + y = 66 →
  32. 32.3x + 7y = 32 and 7x + 3y = 48 →
  33. 33.4x + 2y = −24 and 3x − 2y = 3 →
  34. 34.3x + 4y = −23 and 4x − 2y = 28 →
  35. 35.6x + 7y = 105 and 7x + 6y = 103 →
  36. 36.x + 8y = −49 and 8x + y = −77 →
  37. 37.5x + 4y = 60 and 6x + y = 53 →
  38. 38.7x + 4y = 29 and 4x + 7y = 26 →
  39. 39.2x + 3y = 21 and 4x + 2y = 22 →
  40. 40.4x + 5y = 56 and 6x − y = 50 →

Answer key

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

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