← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 475 · 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. 1.5x + 9y = 55 and 9x + 5y = 43 →
  2. 2.x + 6y = 15 and 5x + 6y = 27 →
  3. 3.9x + 7y = 58 and 7x + 9y = 70 →
  4. 4.2x + 5y = 51 and 5x + y = 47 →
  5. 5.x + 3y = −32 and 3x + y = −24 →
  6. 6.8x + 6y = −56 and 6x + 8y = −56 →
  7. 7.7x + 6y = −10 and 6x + 7y = −3 →
  8. 8.3x + 6y = 24 and 6x − 6y = 30 →
  9. 9.5x + 2y = 7 and 4x + 3y = −7 →
  10. 10.9x + 7y = 144 and 7x + 9y = 144 →
  11. 11.5x + 6y = 32 and x + 2y = 8 →
  12. 12.3x + y = 20 and x − 3y = −20 →
  13. 13.4x − 6y = −10 and x − 5y = −13 →
  14. 14.7x + 9y = 46 and 9x + 7y = 50 →
  15. 15.x + y = 7 and 5x − 3y = 11 →
  16. 16.7x + 9y = −95 and 9x + 7y = −81 →
  17. 17.3x + 6y = −51 and 5x + 2y = −13 →
  18. 18.3x − 6y = 30 and x − 4y = 28 →
  19. 19.8x + 5y = 48 and 5x + 8y = 69 →
  20. 20.3x + y = 12 and x + 3y = −20 →
  21. 21.4x + 5y = 41 and 4x + 6y = 42 →
  22. 22.x + 2y = 16 and 5x − 2y = 8 →
  23. 23.4x + 8y = 8 and 8x + 4y = −44 →
  24. 24.5x + 6y = 69 and 2x + 4y = 42 →
  25. 25.2x − y = 9 and 5x − 3y = 20 →
  26. 26.3x + 4y = 51 and 5x + 3y = 63 →
  27. 27.3x + 4y = 16 and 2x − 5y = 3 →
  28. 28.8x + 5y = −35 and 5x + 8y = −17 →
  29. 29.x + 9y = −55 and 9x + y = −15 →
  30. 30.4x − 4y = 0 and 4x + 4y = 24 →
  31. 31.4x − 4y = −16 and 4x + 2y = 38 →
  32. 32.2x + 7y = −26 and 7x + 2y = −1 →
  33. 33.5x + 2y = −13 and 2x + 5y = 20 →
  34. 34.3x − 4y = −4 and 3x + 3y = −18 →
  35. 35.x + 5y = −38 and 6x + y = 4 →
  36. 36.2x + 3y = 5 and x − 2y = −8 →
  37. 37.9x + 6y = 84 and 6x + 9y = 96 →
  38. 38.2x + 6y = −60 and 5x − 3y = −24 →
  39. 39.5x + 4y = 29 and x + 3y = 8 →
  40. 40.x − 6y = −40 and x + y = 2 →

Answer key

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

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