← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 70 · 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 + 9y = 93 and 9x + 2y = 72 →
  2. 2.3x + 6y = 9 and 6x + 2y = −12 →
  3. 3.2x + 3y = 30 and 3x + 5y = 47 →
  4. 4.4x + y = 15 and 2x − y = 15 →
  5. 5.6x − 4y = 74 and 6x + 5y = 29 →
  6. 6.3x + 3y = 33 and 5x − 3y = −17 →
  7. 7.x + y = 6 and 6x + y = 51 →
  8. 8.6x + y = 17 and 2x − 3y = −11 →
  9. 9.x + 2y = 8 and 3x + y = −6 →
  10. 10.5x + 3y = 41 and 4x + 2y = 32 →
  11. 11.3x + y = −20 and 3x − 6y = −48 →
  12. 12.4x + 2y = 26 and 5x + 2y = 28 →
  13. 13.6x + 6y = −6 and 4x + y = −10 →
  14. 14.5x − 2y = 6 and x + 4y = 10 →
  15. 15.7x + 4y = −11 and 4x + 7y = 22 →
  16. 16.x + 4y = 5 and 4x + y = −10 →
  17. 17.3x − y = 8 and 5x − 3y = 20 →
  18. 18.2x + 5y = −15 and 5x + 2y = −27 →
  19. 19.x + 6y = 32 and 6x + y = 17 →
  20. 20.3x + 6y = −39 and 6x + 3y = −6 →
  21. 21.2x + 5y = 21 and 5x + 4y = 10 →
  22. 22.5x + 9y = 112 and 9x + 5y = 112 →
  23. 23.5x + 2y = 55 and 2x − 2y = 8 →
  24. 24.2x + 3y = 2 and 5x − 4y = −18 →
  25. 25.5x − 6y = 17 and 6x + 2y = −44 →
  26. 26.4x + 2y = −6 and 2x + 4y = 24 →
  27. 27.9x + 6y = 39 and 6x + 9y = 36 →
  28. 28.4x + y = 20 and 3x − 5y = −31 →
  29. 29.5x + 9y = −51 and 9x + 5y = −47 →
  30. 30.9x + 4y = 13 and 4x + 9y = −52 →
  31. 31.x + 6y = 28 and 6x + y = 28 →
  32. 32.x + 6y = 41 and x + y = 1 →
  33. 33.3x − 3y = −24 and x + 4y = 27 →
  34. 34.6x − 3y = 6 and 3x + 2y = 10 →
  35. 35.3x − y = 4 and 5x − y = 8 →
  36. 36.x − 5y = 1 and 6x + 4y = 40 →
  37. 37.4x − 5y = 59 and 6x − y = 43 →
  38. 38.3x + 2y = 12 and 2x + 3y = 13 →
  39. 39.2x − 3y = 4 and 6x − 2y = 26 →
  40. 40.8x + 9y = −25 and 9x + 8y = −26 →

Answer key

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

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