← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 781 · 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 − 6y = −46 and 4x + 3y = 32 →
  2. 2.6x + 4y = −8 and 4x + 6y = 18 →
  3. 3.5x + 3y = 22 and 3x + y = 18 →
  4. 4.6x + 3y = 81 and 6x + 2y = 72 →
  5. 5.3x + 5y = 30 and x + 5y = 20 →
  6. 6.x − 2y = −8 and 2x + 2y = −10 →
  7. 7.x + 3y = −16 and 2x + y = 8 →
  8. 8.x + 4y = −9 and 4x + y = −21 →
  9. 9.x + 3y = 7 and 5x + 4y = 13 →
  10. 10.x + 6y = 37 and 5x + 2y = 45 →
  11. 11.2x − 2y = 6 and 3x + 3y = 21 →
  12. 12.7x + 2y = 18 and 2x + 7y = 18 →
  13. 13.4x + 5y = −9 and 2x + 5y = −27 →
  14. 14.5x + 6y = 32 and 3x + 4y = 22 →
  15. 15.2x + 3y = −9 and 3x + 2y = 9 →
  16. 16.5x − y = 39 and 5x + 3y = 43 →
  17. 17.7x + 6y = 54 and 6x + 7y = 50 →
  18. 18.4x + 6y = 46 and 6x − y = −1 →
  19. 19.6x + 3y = 27 and x − 3y = 1 →
  20. 20.2x + 6y = 14 and x + 5y = 9 →
  21. 21.x + y = 4 and 5x − 4y = 65 →
  22. 22.2x + 2y = 26 and 4x + y = 28 →
  23. 23.3x + 6y = 24 and 6x + 3y = 3 →
  24. 24.4x + 2y = 10 and 4x + 5y = −17 →
  25. 25.x − 2y = 14 and x + 4y = −34 →
  26. 26.3x + 2y = 33 and 6x + 5y = 75 →
  27. 27.9x + 4y = 64 and 4x + 9y = 14 →
  28. 28.6x − 6y = 18 and 2x + 3y = 31 →
  29. 29.4x + 4y = 24 and x − y = −12 →
  30. 30.5x + y = 14 and 4x + 5y = 49 →
  31. 31.2x − 3y = 8 and x − 4y = 14 →
  32. 32.2x − 4y = −16 and 4x − 3y = −27 →
  33. 33.3x + y = 10 and 4x + y = 13 →
  34. 34.4x + 7y = −40 and 7x + 4y = −4 →
  35. 35.2x + 6y = 38 and 6x + 2y = −30 →
  36. 36.x + 2y = 23 and 2x + y = 19 →
  37. 37.8x + 4y = 76 and 4x + 8y = 92 →
  38. 38.x + 3y = 36 and 3x + 4y = 63 →
  39. 39.5x − 2y = −47 and 3x − 3y = −30 →
  40. 40.6x + y = 14 and 6x + 6y = −6 →

Answer key

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

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