← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 409 · 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 = −7 and 3x + 5y = −23 →
  2. 2.6x − y = 23 and 4x + 4y = −8 →
  3. 3.4x + y = 37 and x + 4y = 43 →
  4. 4.x + 8y = −41 and 8x + y = −13 →
  5. 5.x + 4y = −8 and 4x + y = 28 →
  6. 6.8x + y = 75 and x + 8y = 33 →
  7. 7.3x + 5y = −24 and 5x + 3y = −24 →
  8. 8.3x − 5y = −5 and 3x + 3y = 27 →
  9. 9.3x + 4y = 14 and 2x + 5y = 28 →
  10. 10.6x + 3y = −42 and 3x + 6y = −48 →
  11. 11.6x + 3y = 27 and 3x + 6y = 9 →
  12. 12.x − 2y = 5 and 3x − 2y = 23 →
  13. 13.2x + 2y = 2 and 2x + 4y = 6 →
  14. 14.4x + 9y = 44 and 9x + 4y = 34 →
  15. 15.6x − 3y = 39 and 2x − 3y = 11 →
  16. 16.2x + 5y = 27 and 5x + 2y = −6 →
  17. 17.2x + 6y = −28 and x − 3y = 16 →
  18. 18.5x + 2y = −49 and 2x − 6y = −6 →
  19. 19.x + 5y = −35 and 4x − 4y = 4 →
  20. 20.2x + 6y = 62 and 6x − y = 15 →
  21. 21.x + 4y = 28 and 3x − 2y = 0 →
  22. 22.x + 2y = 8 and 3x + 2y = 20 →
  23. 23.x − y = −8 and 3x + 2y = 21 →
  24. 24.2x + 8y = 26 and 8x + 2y = 14 →
  25. 25.5x + 3y = 2 and 3x + 5y = 14 →
  26. 26.2x + 4y = 26 and 4x + 2y = 22 →
  27. 27.2x + 5y = −27 and 5x + 2y = 27 →
  28. 28.3x + 5y = 39 and 5x + 3y = 33 →
  29. 29.x + 4y = 31 and 4x + y = 4 →
  30. 30.8x + 3y = 39 and 3x + 8y = 49 →
  31. 31.2x + 4y = −44 and 3x + y = −26 →
  32. 32.x + 2y = 16 and 2x + y = 14 →
  33. 33.2x + 3y = 4 and 3x + 2y = 16 →
  34. 34.2x + 5y = −17 and 5x + 2y = −32 →
  35. 35.4x + 3y = 16 and 3x − 3y = −30 →
  36. 36.2x + 8y = 34 and 8x + 2y = −14 →
  37. 37.3x + 3y = 33 and 5x − 4y = −26 →
  38. 38.5x + 6y = −76 and 6x + 5y = −78 →
  39. 39.x − y = 6 and 5x + 5y = 50 →
  40. 40.4x + 2y = −24 and 3x + y = −17 →

Answer key

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

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