← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 74 · 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 − 5y = −23 and x + 5y = 41 →
  2. 2.8x + 5y = 49 and 5x + 8y = 55 →
  3. 3.x + 5y = 31 and 3x + y = 9 →
  4. 4.x + 2y = 5 and 2x + y = 16 →
  5. 5.5x − y = 8 and x + y = 4 →
  6. 6.x + 2y = −15 and 4x − 5y = 44 →
  7. 7.2x + 5y = 16 and 5x + 2y = 19 →
  8. 8.3x + 5y = 39 and 2x + y = 12 →
  9. 9.4x + 2y = −24 and 2x + 4y = 6 →
  10. 10.x + 2y = −13 and 6x − 6y = 12 →
  11. 11.x − 5y = −30 and 3x + 2y = 29 →
  12. 12.x + 3y = −10 and 3x − 5y = −16 →
  13. 13.4x + 3y = 7 and x − y = −7 →
  14. 14.x − 5y = 29 and 4x + 2y = −16 →
  15. 15.x + 2y = 5 and 2x + y = 4 →
  16. 16.6x − 5y = 49 and x + 4y = 13 →
  17. 17.3x − y = 31 and x + 2y = 1 →
  18. 18.6x + y = 36 and x + 6y = 41 →
  19. 19.9x + 2y = 79 and 2x + 9y = 86 →
  20. 20.5x − 5y = −55 and x + y = −3 →
  21. 21.3x + 7y = 68 and 7x + 3y = 52 →
  22. 22.5x − y = 16 and 3x + 6y = 3 →
  23. 23.5x − 6y = 17 and 6x + y = 4 →
  24. 24.5x + 3y = 62 and x − 4y = −29 →
  25. 25.x − 3y = −30 and 2x + 4y = 30 →
  26. 26.8x + 2y = 36 and 2x + 8y = −6 →
  27. 27.4x − 3y = 46 and 3x − 6y = 57 →
  28. 28.x + 5y = 51 and 2x + 6y = 66 →
  29. 29.3x + 6y = 33 and x + 5y = 14 →
  30. 30.4x + 5y = 3 and x + 3y = 6 →
  31. 31.5x + 2y = 27 and 3x + 6y = −27 →
  32. 32.3x + 5y = −6 and x + 4y = 5 →
  33. 33.3x + 4y = 0 and 6x + 2y = 18 →
  34. 34.6x − 4y = 72 and 4x + 5y = 2 →
  35. 35.4x + y = 23 and x + 4y = 17 →
  36. 36.x + 5y = 33 and x − 5y = −47 →
  37. 37.2x + 6y = 66 and 6x + 2y = 70 →
  38. 38.x − 3y = −22 and 2x + 5y = 44 →
  39. 39.2x + 2y = 30 and 2x + 3y = 36 →
  40. 40.2x + 5y = 21 and 2x + y = 17 →

Answer key

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

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