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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 983 · 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. 1.6x + 5y = 84 and 5x + 6y = 81 →
  2. 2.x + 3y = −32 and 3x + y = −24 →
  3. 3.8x + 5y = 83 and 5x + 8y = 86 →
  4. 4.x + 7y = −53 and 7x + y = 13 →
  5. 5.6x + 2y = −20 and 4x + y = −16 →
  6. 6.6x + 5y = 29 and 5x + 6y = 37 →
  7. 7.2x + 8y = −24 and 8x + 2y = 54 →
  8. 8.4x + 2y = −30 and x − 2y = −15 →
  9. 9.5x + 7y = 42 and 7x + 5y = 54 →
  10. 10.2x + 7y = 66 and 7x + 2y = 51 →
  11. 11.x + 5y = −41 and 2x + 4y = −34 →
  12. 12.x + 6y = 29 and 6x + y = 34 →
  13. 13.5x + y = −15 and 2x − y = −13 →
  14. 14.9x + 5y = −78 and 5x + 9y = −62 →
  15. 15.3x + y = −2 and x + 3y = 2 →
  16. 16.x + 5y = 31 and x + 3y = 19 →
  17. 17.6x + 2y = −26 and 2x + 6y = −30 →
  18. 18.4x + 9y = −24 and 9x + 4y = 11 →
  19. 19.6x + 6y = −18 and 3x + 5y = −19 →
  20. 20.4x + 3y = 34 and 2x − y = 12 →
  21. 21.x + 5y = 21 and 6x + 5y = 26 →
  22. 22.6x − 4y = 8 and 6x + 3y = 36 →
  23. 23.2x + 4y = 32 and 5x + y = 26 →
  24. 24.3x − 2y = −4 and 4x + 6y = −14 →
  25. 25.9x + 4y = 35 and 4x + 9y = 30 →
  26. 26.9x + 3y = 63 and 3x + 9y = 93 →
  27. 27.6x − 5y = 69 and 5x + 4y = −16 →
  28. 28.7x + 6y = 61 and 6x + 7y = 56 →
  29. 29.5x − 3y = 56 and 2x + 2y = 0 →
  30. 30.x + 2y = 15 and 3x + y = 10 →
  31. 31.2x − y = 6 and 2x + 2y = 12 →
  32. 32.x + 2y = 14 and 6x − 4y = 36 →
  33. 33.5x + 2y = 1 and 2x + 5y = −8 →
  34. 34.2x + 5y = −12 and 3x + 6y = −12 →
  35. 35.x + 4y = −12 and 4x + y = 12 →
  36. 36.5x + y = 26 and x + 5y = 34 →
  37. 37.3x + 6y = 30 and 4x + 3y = 25 →
  38. 38.4x − 5y = 57 and 2x + 2y = −12 →
  39. 39.5x − y = −13 and 6x + 6y = 42 →
  40. 40.x + 5y = 41 and 5x + y = 37 →

Answer key

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

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