← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 985 · 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. 1.6x − y = 43 and 3x + 2y = 34 →
  2. 2.4x + 2y = 16 and 2x + 4y = 20 →
  3. 3.5x + y = 11 and x + 5y = 7 →
  4. 4.x + 6y = 31 and 2x + 2y = 22 →
  5. 5.x + 3y = 11 and 2x + y = 12 →
  6. 6.6x + y = 51 and 2x + y = 19 →
  7. 7.x + 9y = 47 and 9x + y = 23 →
  8. 8.8x + 9y = −70 and 9x + 8y = −66 →
  9. 9.x − 5y = 21 and x + 2y = −21 →
  10. 10.5x + 3y = 27 and x + 4y = 2 →
  11. 11.8x + 4y = −28 and 4x + 8y = −68 →
  12. 12.5x − y = 12 and 3x + 2y = 28 →
  13. 13.5x + 6y = −73 and 3x + 2y = −31 →
  14. 14.x + 7y = 63 and 7x + y = 57 →
  15. 15.2x + 5y = 4 and 2x − 2y = −10 →
  16. 16.6x + 5y = −8 and 2x − y = −8 →
  17. 17.2x − 2y = 18 and 2x + y = 6 →
  18. 18.4x + y = 1 and x + y = −5 →
  19. 19.6x − 3y = −12 and x − y = −5 →
  20. 20.5x + 3y = −14 and 3x + 2y = −8 →
  21. 21.x + 8y = −24 and 8x + y = 60 →
  22. 22.2x − 5y = −44 and 3x + 5y = 34 →
  23. 23.2x − 6y = 10 and 6x + 5y = −62 →
  24. 24.4x + 5y = 57 and 5x − 3y = 25 →
  25. 25.6x + 9y = −51 and 9x + 6y = −24 →
  26. 26.9x + 2y = 83 and 2x + 9y = 27 →
  27. 27.x + 5y = −46 and 2x − 3y = 12 →
  28. 28.3x + 2y = 25 and 3x − 4y = 13 →
  29. 29.4x + 2y = −40 and 2x + 4y = −32 →
  30. 30.3x + 5y = 67 and 5x + 3y = 69 →
  31. 31.5x + 4y = 19 and 4x − 3y = 9 →
  32. 32.6x + 2y = 72 and 2x − 5y = −27 →
  33. 33.x − y = 8 and 3x − 2y = 17 →
  34. 34.x + 5y = −48 and 5x − 4y = 21 →
  35. 35.3x + y = 4 and 2x − 5y = −3 →
  36. 36.3x + 5y = 15 and 4x − 3y = −38 →
  37. 37.3x + 5y = −1 and 5x + 3y = −23 →
  38. 38.5x + 4y = −9 and 6x + 5y = −10 →
  39. 39.5x + 4y = 66 and 4x + 5y = 69 →
  40. 40.x + 2y = 9 and 2x + y = 15 →

Answer key

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

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