← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 811 · 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.x + 2y = 9 and 3x − 4y = −3 →
  2. 2.9x + 5y = 57 and 5x + 9y = 69 →
  3. 3.2x + 5y = 11 and 5x + 2y = 17 →
  4. 4.3x + 3y = 12 and 2x − 6y = 48 →
  5. 5.x + 3y = 11 and 3x + y = 17 →
  6. 6.3x + 8y = −67 and 8x + 3y = −87 →
  7. 7.5x + 6y = −9 and 3x − 6y = 81 →
  8. 8.8x + 6y = 30 and 6x + 8y = 12 →
  9. 9.3x + 5y = −4 and 3x − 6y = 18 →
  10. 10.2x + 6y = 26 and 4x − 2y = −46 →
  11. 11.3x + 6y = 21 and 6x + 3y = −30 →
  12. 12.2x − 3y = −16 and 5x + 4y = 29 →
  13. 13.3x + 6y = 66 and 4x − 5y = −3 →
  14. 14.5x − 5y = 35 and 2x + 6y = −18 →
  15. 15.5x + 6y = 18 and 3x + 6y = 6 →
  16. 16.4x + 2y = 30 and 3x + y = 20 →
  17. 17.8x + y = 43 and x + 8y = 29 →
  18. 18.6x + 3y = −12 and 3x + 5y = −34 →
  19. 19.8x + y = 17 and x + 8y = 10 →
  20. 20.5x + y = −24 and 2x − 2y = −12 →
  21. 21.5x − 5y = 30 and 4x + 3y = 45 →
  22. 22.3x + y = 25 and 4x − y = 17 →
  23. 23.7x + 6y = 13 and 6x + 7y = 26 →
  24. 24.6x − y = −14 and x + 6y = 10 →
  25. 25.5x + 3y = −28 and 3x + 4y = −19 →
  26. 26.3x + 3y = −3 and 3x + y = −11 →
  27. 27.x + 5y = 13 and 3x − y = 7 →
  28. 28.2x − 6y = −8 and 2x + 4y = 12 →
  29. 29.4x + 2y = 10 and x + 5y = −29 →
  30. 30.7x + 6y = −17 and 6x + 7y = −9 →
  31. 31.3x + 3y = 42 and 4x + y = 38 →
  32. 32.6x + 2y = 44 and 5x + 6y = 54 →
  33. 33.4x − 2y = 14 and 3x + 2y = −7 →
  34. 34.6x + 2y = 22 and 5x + 2y = 19 →
  35. 35.6x + 4y = −22 and x − 4y = −13 →
  36. 36.5x + 3y = −15 and 2x − 5y = −37 →
  37. 37.x + y = 1 and 3x + 5y = 7 →
  38. 38.5x − 2y = 46 and 6x − 6y = 66 →
  39. 39.x + 2y = 1 and 2x + 3y = −3 →
  40. 40.4x + 6y = 36 and 5x + y = 19 →

Answer key

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

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