← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 459 · 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. 1.8x + 7y = 39 and 7x + 8y = 36 →
  2. 2.8x + 4y = 60 and 4x + 8y = 84 →
  3. 3.4x − 3y = −31 and 6x − 6y = −48 →
  4. 4.7x + 9y = 130 and 9x + 7y = 126 →
  5. 5.2x − y = 10 and 6x + 4y = −12 →
  6. 6.4x + y = 8 and 5x + y = 12 →
  7. 7.6x + 3y = 9 and 3x + 6y = 45 →
  8. 8.5x + y = −12 and x + 4y = 9 →
  9. 9.9x + y = −73 and x + 9y = −17 →
  10. 10.2x − 5y = −44 and 5x + 3y = 14 →
  11. 11.3x + 4y = −8 and 2x + 2y = −6 →
  12. 12.x + 2y = 5 and 6x − 3y = 15 →
  13. 13.4x − 3y = −12 and 4x + 5y = 52 →
  14. 14.2x + 2y = −10 and 5x − 5y = 15 →
  15. 15.6x − 3y = 12 and 6x + 3y = 48 →
  16. 16.x + y = 0 and 4x − 4y = 56 →
  17. 17.3x − 2y = 21 and 5x + y = 48 →
  18. 18.3x + 2y = 29 and 2x + 3y = 21 →
  19. 19.4x + 4y = −24 and 2x + y = −5 →
  20. 20.3x + 2y = 13 and 3x + 6y = 33 →
  21. 21.x + 5y = 11 and 4x − 6y = −8 →
  22. 22.x + 5y = 23 and 3x + 3y = 21 →
  23. 23.3x + y = 5 and 2x + y = 3 →
  24. 24.x − y = −5 and 4x − y = 7 →
  25. 25.4x + 3y = −33 and x + 4y = −31 →
  26. 26.4x − 6y = 76 and 5x + 2y = 19 →
  27. 27.2x + 3y = −5 and 3x + 2y = −10 →
  28. 28.3x + 7y = 13 and 7x + 3y = 17 →
  29. 29.2x + y = 10 and 2x + 5y = 18 →
  30. 30.5x + 6y = 14 and x − y = −17 →
  31. 31.9x + 5y = 23 and 5x + 9y = −37 →
  32. 32.3x + 8y = −50 and 8x + 3y = −5 →
  33. 33.4x − 6y = −44 and 2x + 4y = 34 →
  34. 34.4x + 4y = 56 and 6x + 2y = 56 →
  35. 35.2x − 2y = 0 and 5x + y = 54 →
  36. 36.4x − 6y = −34 and 5x − y = 16 →
  37. 37.8x + 2y = −54 and 2x + 8y = −6 →
  38. 38.3x + y = −12 and x + 3y = −28 →
  39. 39.6x + 5y = 70 and 2x − 2y = −6 →
  40. 40.5x − 4y = −51 and x + y = −3 →

Answer key

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

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