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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 321 · 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. 1.7x + 3y = 10 and 3x + 7y = 10 →
  2. 2.2x + y = 21 and 5x + y = 39 →
  3. 3.2x + 5y = −48 and 5x + 2y = −57 →
  4. 4.7x + y = 45 and x + 7y = 27 →
  5. 5.4x − 2y = −30 and 6x + 4y = −24 →
  6. 6.8x + 4y = 32 and 4x + 8y = 52 →
  7. 7.5x + 3y = −52 and x − 2y = 13 →
  8. 8.x + 5y = 32 and 2x + 3y = 29 →
  9. 9.6x + 5y = −3 and 5x + 6y = −8 →
  10. 10.2x + 5y = 11 and 5x + 2y = 17 →
  11. 11.3x + 3y = 15 and 3x + y = 9 →
  12. 12.5x + 8y = −63 and 8x + 5y = −54 →
  13. 13.4x + 4y = −4 and 2x − 6y = −58 →
  14. 14.5x + 2y = −18 and 2x + 3y = −16 →
  15. 15.x + 8y = −1 and 8x + y = 55 →
  16. 16.2x + 4y = 40 and 3x − y = −3 →
  17. 17.x + 5y = 22 and 5x + y = 14 →
  18. 18.6x + 4y = 68 and 3x + 6y = 66 →
  19. 19.x + 4y = −6 and 6x + 3y = 6 →
  20. 20.6x + y = 26 and 3x + 4y = −1 →
  21. 21.6x + 5y = −4 and 6x − y = 44 →
  22. 22.3x + 6y = 42 and x + 4y = 24 →
  23. 23.2x − 6y = 8 and 3x − 2y = −2 →
  24. 24.x + 7y = 44 and 7x + y = 20 →
  25. 25.6x + 4y = 32 and 4x − 3y = −7 →
  26. 26.2x + 9y = −48 and 9x + 2y = −62 →
  27. 27.x + 3y = 24 and x − 3y = −30 →
  28. 28.2x + 6y = 64 and 6x + 2y = 64 →
  29. 29.3x − 2y = −4 and x + 2y = −12 →
  30. 30.2x + y = 2 and x + 2y = −8 →
  31. 31.x + 6y = −47 and 2x − 6y = 50 →
  32. 32.6x + 5y = −82 and 3x − 2y = −5 →
  33. 33.3x + 7y = 13 and 7x + 3y = 57 →
  34. 34.2x + 5y = 11 and 3x − 6y = −24 →
  35. 35.5x + 3y = 26 and 3x + 5y = 38 →
  36. 36.6x + y = 28 and x − 2y = 22 →
  37. 37.6x − 5y = −24 and 4x + 4y = 28 →
  38. 38.6x + 2y = −6 and 2x + 6y = 14 →
  39. 39.4x + 2y = −26 and 4x − 6y = −50 →
  40. 40.3x + 2y = 21 and 2x + 3y = 19 →

Answer key

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

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