← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 200 · 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 = 30 and 6x + y = 13 →
  2. 2.2x − 4y = 24 and 3x + 4y = 16 →
  3. 3.x + 3y = 10 and 3x + y = −10 →
  4. 4.x + 4y = 21 and 2x − 3y = −35 →
  5. 5.3x − 6y = −66 and 3x + 6y = 42 →
  6. 6.2x + 3y = 36 and 3x + 2y = 34 →
  7. 7.6x + 8y = 40 and 8x + 6y = 44 →
  8. 8.6x + 9y = −30 and 9x + 6y = −15 →
  9. 9.2x + 4y = 20 and 4x + 4y = 36 →
  10. 10.5x + 4y = −5 and 4x + 5y = 5 →
  11. 11.5x + 6y = 31 and x + 5y = 10 →
  12. 12.6x + y = 16 and x + 6y = 26 →
  13. 13.6x + 3y = 57 and 3x + 6y = 60 →
  14. 14.3x − 2y = 29 and 6x + y = 38 →
  15. 15.6x + 3y = −75 and 3x + 6y = −69 →
  16. 16.2x − 5y = 0 and 2x + y = 12 →
  17. 17.6x − 5y = 11 and x + 6y = 36 →
  18. 18.4x + 2y = 0 and 6x − y = −16 →
  19. 19.2x − 2y = −2 and 5x − 6y = −11 →
  20. 20.2x + 4y = 16 and 5x − 2y = 16 →
  21. 21.x + 2y = −2 and x + 5y = 7 →
  22. 22.3x − 2y = −14 and 5x + 5y = −15 →
  23. 23.x + 9y = 35 and 9x + y = 75 →
  24. 24.2x + 4y = 14 and x + 3y = 8 →
  25. 25.x + 8y = −9 and 8x + y = 54 →
  26. 26.5x − 6y = 14 and 5x + y = −14 →
  27. 27.4x + 3y = −29 and x + 5y = −20 →
  28. 28.6x + y = 43 and x − y = −1 →
  29. 29.x − 5y = 40 and x + y = −2 →
  30. 30.3x + y = −18 and 4x − y = −31 →
  31. 31.2x + 3y = 32 and 6x + 3y = 60 →
  32. 32.x + 6y = 0 and 6x + y = 35 →
  33. 33.7x + 8y = −17 and 8x + 7y = −13 →
  34. 34.6x + 2y = 56 and 4x + 6y = 42 →
  35. 35.4x + y = 33 and 2x + 2y = 30 →
  36. 36.5x − 2y = 3 and 5x − 5y = −15 →
  37. 37.4x + 6y = 58 and 5x + 3y = 32 →
  38. 38.3x + y = −16 and x + 4y = 13 →
  39. 39.x − 4y = 16 and 6x + 6y = −54 →
  40. 40.2x + 4y = −36 and 3x + y = −14 →

Answer key

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

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