← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 465 · 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. 1.5x + 2y = 32 and x + y = 10 →
  2. 2.6x + 2y = 56 and 6x + 5y = 59 →
  3. 3.9x + 5y = 51 and 5x + 9y = 47 →
  4. 4.5x + 7y = 16 and 7x + 5y = 8 →
  5. 5.2x + y = 20 and 4x − y = 22 →
  6. 6.x + 2y = −13 and x − 2y = 3 →
  7. 7.x − 3y = −8 and 6x + 2y = 12 →
  8. 8.6x − y = 36 and x + 4y = 31 →
  9. 9.6x + 5y = 29 and 2x − 4y = −30 →
  10. 10.2x − 2y = −6 and 2x + 2y = 26 →
  11. 11.x − 6y = 14 and 5x + 2y = 38 →
  12. 12.x + 9y = 43 and 9x + y = 67 →
  13. 13.2x + 5y = 41 and 5x + 6y = 57 →
  14. 14.2x + 4y = 0 and 4x + 2y = −6 →
  15. 15.4x + 4y = 28 and 4x + 3y = 23 →
  16. 16.5x − y = −23 and 5x + 3y = 9 →
  17. 17.7x + 5y = 41 and 5x + 7y = 43 →
  18. 18.8x + 5y = 64 and 5x + 8y = 79 →
  19. 19.8x + 2y = 56 and 2x + 8y = 74 →
  20. 20.6x + 2y = −48 and 5x + 6y = −27 →
  21. 21.x − 2y = 12 and 4x − 2y = 18 →
  22. 22.3x + 6y = 69 and 6x + 3y = 75 →
  23. 23.6x + 2y = 50 and 6x + 6y = 54 →
  24. 24.4x + 3y = 55 and 3x + 4y = 57 →
  25. 25.6x − y = 8 and 3x + 5y = −7 →
  26. 26.6x − y = −10 and 3x + 4y = 13 →
  27. 27.6x − 3y = −36 and 6x + 4y = 6 →
  28. 28.8x + 3y = 22 and 3x + 8y = 22 →
  29. 29.4x + y = 13 and x + 4y = −8 →
  30. 30.8x + 3y = 2 and 3x + 8y = −13 →
  31. 31.x + 9y = −25 and 9x + y = 15 →
  32. 32.2x + 2y = −14 and x − 5y = −19 →
  33. 33.x + 4y = −1 and 2x + 3y = −12 →
  34. 34.x + 5y = 26 and x + 4y = 19 →
  35. 35.2x − 2y = −4 and 4x + 5y = 64 →
  36. 36.2x − 5y = −1 and 3x + 3y = 30 →
  37. 37.2x + 3y = 24 and 2x + 2y = 20 →
  38. 38.2x + 3y = −16 and 2x + 6y = −22 →
  39. 39.x + 4y = 3 and 4x + y = −18 →
  40. 40.5x + 3y = −18 and 6x + 3y = −27 →

Answer key

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

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