← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 365 · 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 + 2y = −6 and 2x + 3y = −1 →
  2. 2.6x − 2y = −62 and 2x + 3y = 5 →
  3. 3.3x − 4y = 23 and 4x − 5y = 29 →
  4. 4.3x + 5y = −64 and 6x + 2y = −64 →
  5. 5.7x + y = 57 and x + 7y = 15 →
  6. 6.8x + 3y = −23 and 3x + 8y = 12 →
  7. 7.x − 3y = −7 and 2x + y = 7 →
  8. 8.5x + 6y = −1 and 6x + 5y = 1 →
  9. 9.x + 5y = 23 and 3x + y = 27 →
  10. 10.6x + 2y = −16 and 2x + 6y = 16 →
  11. 11.3x + 4y = −40 and 4x + 5y = −52 →
  12. 12.x + 6y = −15 and x − 4y = −5 →
  13. 13.6x + 4y = −82 and 4x − y = −29 →
  14. 14.2x + 3y = −16 and 4x + 2y = −8 →
  15. 15.5x − 6y = 58 and 2x − 3y = 28 →
  16. 16.6x + 5y = −16 and 5x + 6y = −17 →
  17. 17.4x − 5y = −41 and 6x + 3y = 33 →
  18. 18.3x + y = −1 and x + 3y = 21 →
  19. 19.4x + 2y = 46 and 4x + 3y = 55 →
  20. 20.6x − y = −9 and 6x + 6y = 12 →
  21. 21.2x − y = 9 and 6x − 2y = 24 →
  22. 22.5x − 3y = 18 and 5x + 2y = 38 →
  23. 23.4x + 2y = 48 and 2x − 2y = 6 →
  24. 24.x + 6y = 50 and 6x + y = −15 →
  25. 25.2x + 6y = 18 and 6x + 2y = 38 →
  26. 26.x − y = −1 and 3x + y = −19 →
  27. 27.x + y = −4 and 5x + 3y = −8 →
  28. 28.2x + y = 11 and 6x + 5y = 47 →
  29. 29.9x + 5y = 31 and 5x + 9y = 11 →
  30. 30.2x + 5y = −54 and 5x + 2y = −51 →
  31. 31.2x + 3y = −34 and 6x + 3y = −66 →
  32. 32.3x + 7y = −6 and 7x + 3y = 26 →
  33. 33.x + 5y = 16 and 6x + 3y = 15 →
  34. 34.x + 2y = 6 and 4x + 3y = 4 →
  35. 35.4x + 2y = 6 and 2x + 5y = 7 →
  36. 36.4x + y = −13 and 6x − y = −37 →
  37. 37.8x + y = −1 and x + 8y = −71 →
  38. 38.3x + 7y = −11 and 7x + 3y = 1 →
  39. 39.4x + 4y = −24 and 3x + 2y = −14 →
  40. 40.9x + y = 23 and x + 9y = 47 →

Answer key

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

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