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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 717 · 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 + y = −3 and 3x − 3y = 27 →
  2. 2.8x + 6y = 112 and 6x + 8y = 112 →
  3. 3.x + 2y = 12 and 2x + y = −3 →
  4. 4.2x + 6y = 24 and 6x + 2y = −24 →
  5. 5.3x − y = 32 and 3x + 2y = 17 →
  6. 6.2x + y = −1 and 2x − 6y = −64 →
  7. 7.2x + y = −6 and x + 2y = 3 →
  8. 8.2x + 5y = 53 and 2x + 4y = 44 →
  9. 9.3x + 9y = −99 and 9x + 3y = −105 →
  10. 10.2x − 3y = 0 and 6x + 5y = 28 →
  11. 11.x + 9y = −23 and 9x + y = 33 →
  12. 12.4x + 6y = 18 and 6x + 4y = 22 →
  13. 13.x − 5y = 15 and 4x + 4y = −36 →
  14. 14.2x + 6y = 10 and 5x − 3y = 7 →
  15. 15.2x + 5y = 47 and 2x + 2y = 20 →
  16. 16.3x + 2y = 26 and 3x + y = 19 →
  17. 17.4x − 5y = −24 and 2x + y = 2 →
  18. 18.5x − y = 11 and 4x + 4y = 52 →
  19. 19.8x + 9y = 21 and 9x + 8y = 13 →
  20. 20.x + 2y = −24 and 5x + y = −39 →
  21. 21.4x + y = −16 and x + 4y = 26 →
  22. 22.2x + 7y = 11 and 7x + 2y = 16 →
  23. 23.2x + 3y = 17 and 2x + y = 7 →
  24. 24.2x + 4y = 16 and 2x − 4y = −24 →
  25. 25.3x + 6y = −27 and x − y = 3 →
  26. 26.4x + 2y = 44 and 2x + 4y = 46 →
  27. 27.2x + 8y = −40 and 8x + 2y = 20 →
  28. 28.2x + 2y = −6 and 4x + 6y = −8 →
  29. 29.4x − 5y = −31 and 6x + 3y = 27 →
  30. 30.5x + 7y = 36 and 7x + 5y = 12 →
  31. 31.5x + 3y = 18 and 3x − 6y = 3 →
  32. 32.x + 3y = −30 and 3x + 4y = −45 →
  33. 33.x + 5y = 40 and 2x − 5y = −25 →
  34. 34.2x + 5y = −44 and 2x + 2y = −20 →
  35. 35.x − 4y = −9 and 5x − 5y = 15 →
  36. 36.2x − 2y = −20 and 4x + 2y = −16 →
  37. 37.3x + y = 13 and 2x + y = 10 →
  38. 38.6x + 5y = 53 and 5x + 6y = 46 →
  39. 39.4x + 7y = 24 and 7x + 4y = −24 →
  40. 40.2x + 3y = −13 and 2x − y = −9 →

Answer key

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

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