← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 478 · 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.x + y = 18 and 5x + 2y = 63 →
  2. 2.2x − 5y = 13 and x + 3y = 12 →
  3. 3.4x + y = 24 and 5x + 4y = 41 →
  4. 4.x + 2y = −15 and 6x + 2y = −60 →
  5. 5.2x + 6y = 40 and 6x + 2y = 24 →
  6. 6.x + 5y = 23 and 6x + 4y = 34 →
  7. 7.x + 6y = 51 and 5x − y = 38 →
  8. 8.6x − 6y = −36 and 5x + 5y = −10 →
  9. 9.6x + 2y = 66 and 2x + y = 24 →
  10. 10.5x + 3y = 31 and 3x + 4y = 23 →
  11. 11.5x + 6y = 39 and 3x + 2y = 25 →
  12. 12.2x + 6y = 30 and 3x − 5y = 17 →
  13. 13.5x + 7y = −12 and 7x + 5y = −12 →
  14. 14.6x + 2y = 16 and 2x + 6y = 16 →
  15. 15.6x + 4y = −46 and 3x + 4y = −19 →
  16. 16.3x + 5y = −29 and 4x − 4y = 36 →
  17. 17.3x + 6y = 30 and 2x + 6y = 22 →
  18. 18.3x − y = −30 and 6x + 6y = −12 →
  19. 19.2x + 9y = 28 and 9x + 2y = 49 →
  20. 20.8x + y = 20 and x + 8y = −29 →
  21. 21.5x + 4y = −9 and 2x + 4y = 6 →
  22. 22.5x − y = −31 and 2x − 3y = −15 →
  23. 23.9x + 6y = 12 and 6x + 9y = −27 →
  24. 24.3x + 6y = 66 and 4x − y = 25 →
  25. 25.6x + 4y = 42 and 4x + 3y = 29 →
  26. 26.6x + y = 51 and 6x + 6y = 96 →
  27. 27.4x − 6y = 38 and 4x + 6y = −22 →
  28. 28.x + 6y = 62 and 5x − 3y = 13 →
  29. 29.9x + 5y = −60 and 5x + 9y = −52 →
  30. 30.2x + 4y = 12 and 2x + 6y = 14 →
  31. 31.5x − 3y = 34 and 2x + 6y = 28 →
  32. 32.x + 9y = −71 and 9x + y = 1 →
  33. 33.4x + y = −2 and 2x − 2y = −6 →
  34. 34.x + 5y = −48 and 2x + y = −15 →
  35. 35.3x + 2y = 7 and x + 2y = −7 →
  36. 36.6x + 7y = −68 and 7x + 6y = −75 →
  37. 37.x + y = 3 and 6x − 2y = −38 →
  38. 38.x − y = 0 and 2x + 2y = 24 →
  39. 39.x + 4y = 25 and 4x + y = −20 →
  40. 40.x + 3y = 27 and 3x − 5y = −17 →

Answer key

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

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