← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 416 · 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 = 5 and 5x + 2y = 23 →
  2. 2.4x + y = −30 and x + 4y = −30 →
  3. 3.2x + 4y = 20 and 5x + y = 41 →
  4. 4.x + 5y = −26 and 6x + 6y = −36 →
  5. 5.3x + 2y = 5 and 2x + 3y = 5 →
  6. 6.3x − 2y = 0 and 5x + 3y = 57 →
  7. 7.4x + y = 13 and x + 4y = 7 →
  8. 8.6x + 2y = 2 and 2x + 6y = 38 →
  9. 9.8x + 9y = 44 and 9x + 8y = 41 →
  10. 10.6x − 2y = 26 and x − 6y = −41 →
  11. 11.2x − 2y = 26 and 2x + 3y = −4 →
  12. 12.4x + 8y = −44 and 8x + 4y = −16 →
  13. 13.2x + 5y = −11 and x + y = 2 →
  14. 14.x + 2y = −6 and 4x + 4y = 0 →
  15. 15.x + 6y = 40 and 6x + y = −40 →
  16. 16.9x + 3y = 42 and 3x + 9y = −18 →
  17. 17.6x + 2y = −34 and 4x + 4y = −12 →
  18. 18.6x + y = 13 and x + 6y = 8 →
  19. 19.4x − 6y = −8 and 2x − 6y = −22 →
  20. 20.4x + 2y = 18 and 6x + 5y = 9 →
  21. 21.3x + 3y = 15 and 4x + y = −7 →
  22. 22.x + y = 2 and 2x − y = 10 →
  23. 23.5x + 2y = 23 and 6x − 2y = −12 →
  24. 24.5x + 6y = 44 and 2x − 2y = 0 →
  25. 25.6x + 9y = −9 and 9x + 6y = −21 →
  26. 26.6x + y = 57 and 2x − 6y = 0 →
  27. 27.9x + 3y = 99 and 3x + 9y = 81 →
  28. 28.6x + 3y = 45 and 6x − y = 17 →
  29. 29.6x − 4y = 64 and 3x + 2y = 4 →
  30. 30.2x − 2y = −20 and x + y = −2 →
  31. 31.x + 7y = 33 and 7x + y = −57 →
  32. 32.6x + 2y = 26 and 2x + 5y = 39 →
  33. 33.3x + 9y = −102 and 9x + 3y = −90 →
  34. 34.x − 4y = 16 and 2x + 3y = −23 →
  35. 35.2x + 4y = −6 and 4x + 2y = −30 →
  36. 36.4x + 2y = 52 and 2x + 4y = 50 →
  37. 37.5x + 9y = 28 and 9x + 5y = 28 →
  38. 38.2x − 2y = 12 and 3x + 4y = 32 →
  39. 39.x − y = 1 and x + 5y = 49 →
  40. 40.6x + 8y = −8 and 8x + 6y = 22 →

Answer key

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

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