← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 338 · 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 + 4y = 16 and 4x + 3y = 7 →
  2. 2.x + 7y = 64 and 7x + y = 16 →
  3. 3.9x + y = 33 and x + 9y = 57 →
  4. 4.2x + 5y = −20 and 5x + 2y = 13 →
  5. 5.x + 3y = −29 and 3x + y = −23 →
  6. 6.5x − y = 6 and x − 3y = 4 →
  7. 7.4x + 5y = −51 and 5x + 4y = −57 →
  8. 8.3x + 3y = 3 and 6x + 2y = 26 →
  9. 9.x + 2y = 1 and 5x + 2y = 29 →
  10. 10.6x + 5y = 43 and x − 2y = −7 →
  11. 11.4x + 5y = −5 and 3x − 6y = 45 →
  12. 12.8x + 7y = −82 and 7x + 8y = −83 →
  13. 13.2x + 4y = −12 and 4x + 2y = −30 →
  14. 14.5x + 5y = 35 and 3x + 6y = 18 →
  15. 15.8x + 9y = −16 and 9x + 8y = −1 →
  16. 16.2x + 3y = −1 and 6x − 5y = 11 →
  17. 17.6x + 4y = 54 and 4x + 6y = 56 →
  18. 18.9x + y = 79 and x + 9y = 71 →
  19. 19.5x + 6y = −55 and 2x − 3y = 5 →
  20. 20.5x + 6y = 57 and x − 3y = −18 →
  21. 21.2x + 8y = 44 and 8x + 2y = 26 →
  22. 22.2x + 7y = −2 and 7x + 2y = −52 →
  23. 23.4x − 3y = −7 and 4x − 5y = −25 →
  24. 24.4x + 3y = 36 and 5x + 6y = 63 →
  25. 25.3x + 5y = −2 and 4x + 4y = 8 →
  26. 26.4x + 2y = 6 and 2x + 2y = 4 →
  27. 27.5x + 3y = 52 and 3x + 5y = 44 →
  28. 28.5x + 6y = −76 and 6x + 5y = −78 →
  29. 29.2x − 5y = 48 and 4x − y = 24 →
  30. 30.4x + 5y = 41 and 2x + y = 13 →
  31. 31.8x + y = 55 and x + 8y = −64 →
  32. 32.4x + 6y = 26 and 6x + 4y = 34 →
  33. 33.x + 3y = 3 and 3x + y = −23 →
  34. 34.8x + 4y = −8 and 4x + 8y = 20 →
  35. 35.4x + 8y = 40 and 8x + 4y = 56 →
  36. 36.4x − 4y = 28 and 5x + 2y = −7 →
  37. 37.2x + 5y = −19 and 5x + 2y = 26 →
  38. 38.2x + 6y = −6 and 3x − 6y = 36 →
  39. 39.3x + 6y = 21 and 4x + 4y = 12 →
  40. 40.5x + 9y = −40 and 9x + 5y = −16 →

Answer key

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

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