← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 547 · 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. 1.4x + 2y = 30 and 3x − 6y = 30 →
  2. 2.8x + 9y = 26 and 9x + 8y = 25 →
  3. 3.6x − 2y = 20 and 5x − 3y = 10 →
  4. 4.5x − 6y = 7 and x + 5y = 20 →
  5. 5.3x + y = −20 and 3x + 2y = −19 →
  6. 6.x + 4y = 3 and x + y = −3 →
  7. 7.3x + 5y = −20 and x − 4y = 33 →
  8. 8.3x − 5y = −61 and 4x + 5y = 12 →
  9. 9.7x + y = 57 and x + 7y = −33 →
  10. 10.3x + 5y = −22 and 6x − 3y = 21 →
  11. 11.x + 2y = −17 and 2x + y = −16 →
  12. 12.4x + 2y = −2 and 2x + 4y = 14 →
  13. 13.4x + 5y = 54 and 5x + 4y = 54 →
  14. 14.x + 2y = 17 and 2x + y = 16 →
  15. 15.6x + 3y = 60 and 3x + 6y = 57 →
  16. 16.3x + 6y = −63 and 3x − 3y = 0 →
  17. 17.5x + 3y = 50 and 4x − 3y = 13 →
  18. 18.5x + y = −22 and x + 4y = −31 →
  19. 19.4x − y = 24 and 5x + 2y = 56 →
  20. 20.6x + 5y = 36 and 3x − 6y = −33 →
  21. 21.2x − 2y = 12 and 3x − 2y = 15 →
  22. 22.5x − y = 13 and 6x − 2y = 22 →
  23. 23.6x − y = 1 and 4x − 5y = 31 →
  24. 24.5x + 4y = 48 and 4x + 5y = 42 →
  25. 25.5x + y = 45 and x − y = 3 →
  26. 26.6x − y = 40 and 3x + 4y = 29 →
  27. 27.4x + 2y = 26 and 4x + y = 19 →
  28. 28.4x − 5y = −20 and 5x + 5y = 65 →
  29. 29.3x + 6y = 0 and 6x + y = −44 →
  30. 30.5x + 3y = −2 and x − 4y = 41 →
  31. 31.2x + y = 23 and 2x − y = 9 →
  32. 32.4x + y = 3 and x + 4y = −33 →
  33. 33.6x + y = −30 and 5x − 4y = −54 →
  34. 34.3x + 2y = 13 and 6x − y = 1 →
  35. 35.4x + 4y = −16 and 5x + 4y = −21 →
  36. 36.4x − 2y = 30 and x + 5y = 13 →
  37. 37.x + 3y = −4 and 3x + y = 20 →
  38. 38.7x + 9y = −44 and 9x + 7y = −20 →
  39. 39.8x + 7y = 25 and 7x + 8y = 35 →
  40. 40.4x + 8y = 36 and 8x + 4y = 48 →

Answer key

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

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