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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 22 · 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. 1.9x + 7y = 74 and 7x + 9y = 86 →
  2. 2.8x + 5y = 44 and 5x + 8y = 8 →
  3. 3.x + 5y = 29 and 5x + y = 49 →
  4. 4.5x + 3y = 21 and 3x + 5y = 3 →
  5. 5.5x + 4y = 31 and x + 6y = 27 →
  6. 6.5x + 3y = −57 and x − 5y = 11 →
  7. 7.6x + y = 33 and 3x + 4y = 27 →
  8. 8.5x − 2y = −7 and x + 6y = 37 →
  9. 9.x + 3y = 17 and 3x + y = 11 →
  10. 10.4x + 6y = 16 and 6x + 4y = −16 →
  11. 11.3x + 3y = 9 and 3x + 2y = 5 →
  12. 12.6x − 6y = −24 and x + 4y = 36 →
  13. 13.2x + 9y = 80 and 9x + 2y = 52 →
  14. 14.5x + y = 12 and 3x + 4y = −3 →
  15. 15.6x + 2y = 40 and x − 5y = 12 →
  16. 16.8x + 5y = 57 and 5x + 8y = 60 →
  17. 17.3x + 2y = 17 and 2x + 3y = 18 →
  18. 18.6x + 7y = −12 and 7x + 6y = −1 →
  19. 19.2x − y = 5 and x + 6y = 48 →
  20. 20.x − 3y = 25 and 3x + y = −15 →
  21. 21.9x + 3y = 24 and 3x + 9y = 24 →
  22. 22.3x + y = 21 and 2x − y = 9 →
  23. 23.6x − 5y = 22 and x + 2y = −2 →
  24. 24.x + 5y = −28 and x − 5y = 12 →
  25. 25.2x + 6y = −20 and 3x + 3y = 6 →
  26. 26.5x − 2y = −41 and x − 6y = 3 →
  27. 27.4x − 2y = −16 and 2x + 2y = 4 →
  28. 28.x + 5y = −16 and 6x + 6y = 0 →
  29. 29.2x + 3y = −19 and 3x + 2y = −6 →
  30. 30.7x + 5y = 62 and 5x + 7y = 58 →
  31. 31.3x + y = 12 and 2x − 4y = 36 →
  32. 32.4x + 2y = −12 and 6x + 2y = −14 →
  33. 33.5x + 2y = −28 and 2x + 3y = 2 →
  34. 34.x + y = −8 and 2x + 6y = −12 →
  35. 35.4x + 5y = 13 and x − 6y = −4 →
  36. 36.6x − 4y = 54 and 3x − 6y = 51 →
  37. 37.4x − 3y = 29 and 4x + 5y = 37 →
  38. 38.5x + 3y = 46 and x + 3y = 26 →
  39. 39.6x − 3y = 66 and 2x − 2y = 30 →
  40. 40.3x + 2y = 24 and 2x + 3y = 21 →

Answer key

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

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