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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 742 · 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 = 2 and 3x − 5y = 5 →
  2. 2.5x + 2y = 7 and x − 2y = 11 →
  3. 3.6x − 6y = 54 and 3x − y = 15 →
  4. 4.4x − 2y = 36 and x − 6y = 31 →
  5. 5.6x − y = −6 and x + 6y = −38 →
  6. 6.3x + 3y = 27 and 2x + 3y = 24 →
  7. 7.6x + 5y = 74 and 4x + 2y = 44 →
  8. 8.2x + y = 19 and x + 2y = 23 →
  9. 9.x + 5y = 26 and 4x − 3y = −57 →
  10. 10.5x + 8y = −67 and 8x + 5y = −76 →
  11. 11.2x − 6y = 22 and 4x + y = 18 →
  12. 12.2x + 2y = 0 and 4x − y = −40 →
  13. 13.5x + 3y = −22 and 5x − 5y = −70 →
  14. 14.2x + 3y = 14 and 4x − 6y = −20 →
  15. 15.9x + 2y = −14 and 2x + 9y = 14 →
  16. 16.x + 7y = 59 and 7x + y = 29 →
  17. 17.2x + 2y = −28 and 2x + 6y = −56 →
  18. 18.3x + 4y = −9 and 5x + 5y = −10 →
  19. 19.6x + 6y = −30 and 6x − 2y = −46 →
  20. 20.3x + 2y = −5 and 2x + 3y = −5 →
  21. 21.2x + 2y = −10 and 5x + 2y = −7 →
  22. 22.5x + 9y = 39 and 9x + 5y = 59 →
  23. 23.5x + 6y = 55 and 5x + y = 30 →
  24. 24.3x + 2y = 0 and 2x + 3y = 15 →
  25. 25.3x + 8y = 14 and 8x + 3y = 19 →
  26. 26.8x + 3y = 9 and 3x + 8y = −31 →
  27. 27.4x − 5y = 13 and 5x + 6y = −45 →
  28. 28.6x − 5y = −28 and 3x − 2y = −13 →
  29. 29.3x + 5y = 11 and 5x − 2y = 39 →
  30. 30.6x + 3y = −36 and 3x + 6y = −54 →
  31. 31.x + 5y = 16 and x + 6y = 19 →
  32. 32.2x + 5y = 53 and 6x − 3y = −3 →
  33. 33.9x + y = 49 and x + 9y = 41 →
  34. 34.2x + 3y = −25 and x + 5y = −23 →
  35. 35.x + 2y = −7 and 3x − 5y = 56 →
  36. 36.5x − y = −28 and 4x + y = −8 →
  37. 37.x − 5y = 42 and 2x + y = −4 →
  38. 38.4x − y = −10 and 4x + 2y = −16 →
  39. 39.2x + 3y = −4 and 3x + 2y = −1 →
  40. 40.3x + 5y = 34 and 5x + 3y = 30 →

Answer key

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

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