← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 866 · 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 − 4y = −2 and 5x − 4y = 6 →
  2. 2.6x + 2y = 0 and 2x + 6y = 16 →
  3. 3.5x − 4y = 13 and 5x + y = 53 →
  4. 4.2x + 4y = 32 and 4x + 2y = 28 →
  5. 5.9x + y = 68 and x + 9y = 52 →
  6. 6.5x + 5y = 55 and 2x − y = −5 →
  7. 7.3x − 3y = −33 and 3x − y = −15 →
  8. 8.x − 5y = −23 and 3x + y = 11 →
  9. 9.6x + 2y = 6 and x + 3y = 25 →
  10. 10.8x + 7y = −31 and 7x + 8y = −29 →
  11. 11.4x − 5y = −21 and 2x + y = 21 →
  12. 12.2x + 4y = 8 and 6x − 4y = −24 →
  13. 13.6x − 2y = 28 and 4x + 4y = 24 →
  14. 14.5x + 3y = 6 and 3x + 5y = 26 →
  15. 15.x + 7y = −27 and 7x + y = 51 →
  16. 16.3x − 4y = 12 and 6x + y = 51 →
  17. 17.5x + y = 7 and x + 6y = −16 →
  18. 18.4x − 5y = −11 and 2x + y = −23 →
  19. 19.5x + y = 9 and 4x + 6y = −24 →
  20. 20.2x + 5y = 53 and 5x + 5y = 80 →
  21. 21.5x + 9y = 78 and 9x + 5y = 62 →
  22. 22.x − 5y = 39 and 6x − 4y = 78 →
  23. 23.6x + 4y = −24 and 6x − 6y = −84 →
  24. 24.4x − 6y = −18 and 4x + y = 45 →
  25. 25.x + 6y = −10 and 3x − 5y = 16 →
  26. 26.4x + y = −31 and 5x + 4y = −25 →
  27. 27.x + 6y = 15 and 6x + y = 55 →
  28. 28.3x + 3y = −27 and 3x − 3y = −3 →
  29. 29.6x − y = 55 and 3x + 3y = 24 →
  30. 30.x − 2y = −11 and 3x − 3y = −30 →
  31. 31.x + y = 9 and 2x − 5y = −38 →
  32. 32.3x + 4y = 17 and 4x + 3y = 25 →
  33. 33.4x + 7y = 69 and 7x + 4y = 63 →
  34. 34.9x + 5y = −73 and 5x + 9y = −53 →
  35. 35.4x + 6y = 38 and x + y = 7 →
  36. 36.3x + 5y = 14 and 5x + 3y = 34 →
  37. 37.x + 6y = 49 and 2x − 2y = 0 →
  38. 38.2x + 3y = 15 and 5x + 6y = 39 →
  39. 39.2x + 3y = 15 and 4x − 5y = 19 →
  40. 40.5x + 5y = 50 and x − 2y = 1 →

Answer key

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

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