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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 497 · 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 − 4y = −36 and x + 6y = 46 →
  2. 2.8x + 3y = −43 and 3x + 8y = −78 →
  3. 3.2x + 9y = 73 and 9x + 2y = 59 →
  4. 4.x + y = −4 and x − 2y = −7 →
  5. 5.5x + 5y = 10 and 5x + y = 22 →
  6. 6.4x − 2y = 12 and 3x − y = 13 →
  7. 7.8x + y = 52 and x + 8y = −25 →
  8. 8.4x + 3y = 50 and 2x + y = 22 →
  9. 9.2x + y = −1 and 5x + y = 5 →
  10. 10.6x + 9y = 93 and 9x + 6y = 102 →
  11. 11.4x − 6y = 14 and 2x + 2y = −8 →
  12. 12.4x + 6y = −2 and 6x + 3y = 15 →
  13. 13.4x + 6y = −18 and 2x + y = −11 →
  14. 14.8x + 4y = 16 and 4x + 8y = 20 →
  15. 15.5x + 7y = 93 and 7x + 5y = 87 →
  16. 16.9x + y = 10 and x + 9y = 10 →
  17. 17.6x + y = 47 and 3x + 6y = 51 →
  18. 18.5x + 4y = 30 and 2x + 6y = 34 →
  19. 19.5x + 3y = 28 and 3x + 3y = 18 →
  20. 20.2x + 5y = 17 and 6x + 5y = 41 →
  21. 21.2x + y = 11 and 5x − y = 31 →
  22. 22.6x + 7y = 32 and 7x + 6y = 33 →
  23. 23.5x − 4y = −20 and 4x + 6y = −62 →
  24. 24.3x + y = −18 and x + 3y = −30 →
  25. 25.4x + 2y = 18 and x − 3y = −13 →
  26. 26.6x + y = −9 and x + 6y = 16 →
  27. 27.x + 2y = −4 and 2x + y = −5 →
  28. 28.5x + 3y = 59 and 4x − 6y = −20 →
  29. 29.x − 3y = −20 and 6x − 3y = −15 →
  30. 30.x + 2y = −21 and 5x − 4y = 21 →
  31. 31.5x + 8y = 55 and 8x + 5y = 49 →
  32. 32.3x + y = 23 and x + 3y = 29 →
  33. 33.6x − 5y = 29 and 2x + 3y = 33 →
  34. 34.4x + 5y = −46 and 5x + 4y = −53 →
  35. 35.8x + 7y = −78 and 7x + 8y = −72 →
  36. 36.4x − 2y = 24 and 2x + 2y = 30 →
  37. 37.2x − y = 8 and 2x − 5y = −8 →
  38. 38.3x + 4y = 23 and 4x + 3y = 26 →
  39. 39.2x − 4y = 8 and 2x − 6y = 6 →
  40. 40.3x + 3y = 9 and 6x − y = 60 →

Answer key

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

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