← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 100 · 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. 1.3x + 5y = 63 and x + 5y = 51 →
  2. 2.x − 2y = −25 and x + 5y = 38 →
  3. 3.8x + 6y = 38 and 6x + 8y = 46 →
  4. 4.x + 6y = 26 and 2x − 4y = −28 →
  5. 5.x + 9y = −19 and 9x + y = −11 →
  6. 6.4x + 4y = 44 and 4x + y = 23 →
  7. 7.2x + 3y = −11 and 3x − 6y = 36 →
  8. 8.4x − 4y = 28 and 2x − 6y = 6 →
  9. 9.8x + 6y = 32 and 6x + 8y = 10 →
  10. 10.3x + 4y = 37 and x + y = 10 →
  11. 11.5x + 2y = 63 and x + 2y = 27 →
  12. 12.7x + 9y = 99 and 9x + 7y = 109 →
  13. 13.2x + 7y = 26 and 7x + 2y = 1 →
  14. 14.4x + 4y = −72 and 5x + 2y = −63 →
  15. 15.4x + y = 2 and x + 4y = 23 →
  16. 16.5x + 2y = 0 and 6x − 5y = −37 →
  17. 17.6x + 2y = −30 and 3x − y = −33 →
  18. 18.2x + 8y = −66 and 8x + 2y = 6 →
  19. 19.4x + 6y = 2 and 2x + 2y = 6 →
  20. 20.x + 2y = 11 and 2x + y = 10 →
  21. 21.9x + 7y = −15 and 7x + 9y = −1 →
  22. 22.3x + 4y = −30 and x − 2y = 20 →
  23. 23.6x + 8y = 18 and 8x + 6y = 38 →
  24. 24.4x + 3y = 31 and 3x + 4y = 39 →
  25. 25.x + 6y = 60 and 4x + y = 33 →
  26. 26.5x + 8y = −21 and 8x + 5y = −18 →
  27. 27.8x + y = −18 and x + 8y = −18 →
  28. 28.5x − 3y = −49 and 2x + 3y = −7 →
  29. 29.9x + 2y = 75 and 2x + 9y = 68 →
  30. 30.3x − 2y = 13 and 2x + 4y = 46 →
  31. 31.2x − 2y = 32 and 3x + 6y = −24 →
  32. 32.x − 5y = −37 and 6x − y = −48 →
  33. 33.5x + y = −3 and 4x − 5y = 44 →
  34. 34.8x + 7y = −96 and 7x + 8y = −99 →
  35. 35.5x + 7y = 56 and 7x + 5y = 64 →
  36. 36.3x + 4y = 43 and 3x − 6y = −27 →
  37. 37.2x + y = 19 and x + 2y = 20 →
  38. 38.2x + 5y = 49 and 3x − y = −3 →
  39. 39.4x + 2y = −26 and 2x + 4y = 2 →
  40. 40.3x + 6y = 18 and 5x + 3y = 23 →

Answer key

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

Free vedic maths lessons, practice and worksheets at talentjr.in/vedic-maths