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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 484 · 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 − 2y = 4 and 2x − 3y = 9 →
  2. 2.5x + y = 38 and x + 5y = 46 →
  3. 3.6x + 4y = 18 and 6x − 5y = −9 →
  4. 4.2x + 7y = 45 and 7x + 2y = 45 →
  5. 5.3x − 2y = −6 and x + 5y = 32 →
  6. 6.5x + 5y = 25 and 4x − 4y = 12 →
  7. 7.3x − 4y = 20 and 3x − 5y = 19 →
  8. 8.7x + 5y = −16 and 5x + 7y = 16 →
  9. 9.4x − 3y = −15 and 4x + 3y = 39 →
  10. 10.6x + 2y = −26 and x − 2y = −16 →
  11. 11.2x + 5y = −2 and 5x + 2y = 37 →
  12. 12.4x + 3y = 1 and 3x + 4y = −8 →
  13. 13.6x − 6y = 48 and 6x − 4y = 44 →
  14. 14.2x + 3y = 36 and 2x + 4y = 42 →
  15. 15.5x − 2y = −37 and x + y = 1 →
  16. 16.4x + 3y = 41 and 5x + 3y = 49 →
  17. 17.5x + 4y = 60 and 4x + y = 37 →
  18. 18.6x − 6y = −18 and x − 4y = −15 →
  19. 19.4x + y = 39 and x + 4y = 21 →
  20. 20.4x + y = −20 and 5x − 2y = −51 →
  21. 21.5x + 2y = 18 and 2x + 5y = 24 →
  22. 22.7x + 2y = 28 and 2x + 7y = −37 →
  23. 23.6x + 9y = 66 and 9x + 6y = 84 →
  24. 24.2x + 4y = 42 and 6x + 6y = 84 →
  25. 25.2x + y = 7 and x + 2y = 11 →
  26. 26.6x + 6y = 66 and 2x − 4y = −32 →
  27. 27.7x + 4y = 67 and 4x + 7y = 43 →
  28. 28.2x + 4y = 44 and 4x + 2y = 40 →
  29. 29.7x + 2y = 19 and 2x + 7y = −1 →
  30. 30.3x − y = −20 and 5x − y = −28 →
  31. 31.x + 4y = 32 and 4x + 6y = 68 →
  32. 32.4x + 2y = 28 and 6x + 4y = 44 →
  33. 33.2x + y = 11 and 6x + y = 27 →
  34. 34.3x + 6y = 30 and 5x + y = 23 →
  35. 35.3x + y = 18 and x + 3y = −18 →
  36. 36.2x + y = 7 and x − y = 2 →
  37. 37.3x + 8y = 45 and 8x + 3y = 65 →
  38. 38.3x + 3y = 48 and 4x − 2y = 16 →
  39. 39.x + 5y = 38 and 6x + 2y = 4 →
  40. 40.2x − 4y = −32 and 5x + 3y = 37 →

Answer key

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

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