← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 810 · 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. 1.4x + 3y = 2 and 2x + 4y = −4 →
  2. 2.3x − 6y = −42 and 5x + 2y = 26 →
  3. 3.3x + 4y = 45 and 4x + 3y = 46 →
  4. 4.5x + 5y = 15 and 5x − 4y = −3 →
  5. 5.5x + 5y = 20 and 3x + 5y = 18 →
  6. 6.8x + 7y = 54 and 7x + 8y = 51 →
  7. 7.5x + 6y = 83 and 2x − 6y = −34 →
  8. 8.x + 4y = −43 and 3x − 5y = 24 →
  9. 9.3x − 3y = −54 and 6x + y = −45 →
  10. 10.6x − 5y = −72 and 4x + 4y = −4 →
  11. 11.x − 2y = 15 and 6x − y = 57 →
  12. 12.x − 5y = −8 and x + 2y = 6 →
  13. 13.6x + 9y = 57 and 9x + 6y = 78 →
  14. 14.x + 3y = 17 and 3x + y = 11 →
  15. 15.8x + 9y = −39 and 9x + 8y = −46 →
  16. 16.4x + 6y = 50 and 2x + 6y = 52 →
  17. 17.6x + 2y = −44 and 5x − 5y = −30 →
  18. 18.2x + 9y = 24 and 9x + 2y = 31 →
  19. 19.4x + 6y = 20 and 2x + y = 6 →
  20. 20.4x + 5y = 58 and 5x + 4y = 59 →
  21. 21.x + 5y = −4 and x − 5y = −14 →
  22. 22.2x + 3y = 17 and 3x + 2y = 23 →
  23. 23.4x − 3y = 31 and 3x − 5y = 37 →
  24. 24.6x + 4y = −74 and x − 4y = 25 →
  25. 25.5x − y = 1 and 2x + y = 6 →
  26. 26.2x + 3y = 26 and 3x + 2y = 29 →
  27. 27.6x + 4y = 46 and 4x − 4y = 44 →
  28. 28.4x − 4y = −4 and 6x + 5y = 82 →
  29. 29.3x + 3y = 39 and 4x − y = 27 →
  30. 30.x + 2y = 0 and 6x + 4y = 24 →
  31. 31.4x + 3y = −19 and 6x + 4y = −24 →
  32. 32.5x + 5y = 60 and 5x + 4y = 57 →
  33. 33.4x + y = 19 and 2x + 4y = 34 →
  34. 34.5x + 7y = 34 and 7x + 5y = 38 →
  35. 35.5x + 4y = −22 and x − 4y = −14 →
  36. 36.2x + 2y = −14 and 2x + y = −10 →
  37. 37.6x + 4y = 38 and 3x + 6y = 27 →
  38. 38.6x + 5y = 10 and 5x + 6y = 1 →
  39. 39.4x + 5y = 29 and 5x + 4y = 25 →
  40. 40.x + 3y = 17 and x + 2y = 11 →

Answer key

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

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