← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 685 · 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. 1.9x + y = −35 and x + 9y = −75 →
  2. 2.3x + 3y = 12 and 2x + 4y = 12 →
  3. 3.x + 5y = 22 and x + 4y = 17 →
  4. 4.2x − 6y = −38 and 2x + 3y = 43 →
  5. 5.3x + 2y = −21 and 2x + 3y = −24 →
  6. 6.4x − 4y = −12 and 3x − 4y = −13 →
  7. 7.x + y = −8 and 2x + y = −14 →
  8. 8.3x + 6y = 66 and 6x + 3y = 51 →
  9. 9.5x + 4y = −40 and x + 4y = −24 →
  10. 10.4x + 5y = 13 and 5x + 4y = 5 →
  11. 11.2x − 3y = −4 and 2x − y = 0 →
  12. 12.6x + 6y = 0 and 4x + 6y = −18 →
  13. 13.5x + 3y = 17 and 3x + 5y = 39 →
  14. 14.2x + 3y = −29 and 4x − 3y = 23 →
  15. 15.8x + 6y = 80 and 6x + 8y = 88 →
  16. 16.x + 5y = −29 and 2x − 2y = 14 →
  17. 17.x + 4y = 29 and 3x + 6y = 45 →
  18. 18.5x + 6y = 11 and x + y = 2 →
  19. 19.9x + 7y = 92 and 7x + 9y = 100 →
  20. 20.3x + 5y = 2 and 5x + 6y = 8 →
  21. 21.x + 7y = −60 and 7x + y = 12 →
  22. 22.6x + 4y = 6 and 4x − 2y = 18 →
  23. 23.9x + 4y = 46 and 4x + 9y = 71 →
  24. 24.5x − 3y = −57 and 5x + y = −41 →
  25. 25.3x − y = 9 and 6x + 5y = −3 →
  26. 26.6x + 2y = −12 and x + 2y = 3 →
  27. 27.8x + 6y = −48 and 6x + 8y = −50 →
  28. 28.2x + 4y = 40 and 4x + 2y = 38 →
  29. 29.8x + y = −25 and x + 8y = −74 →
  30. 30.x + y = 10 and 6x − 2y = −12 →
  31. 31.6x + 7y = 3 and 7x + 6y = 10 →
  32. 32.4x + 6y = 70 and 5x + y = 42 →
  33. 33.3x + 4y = 5 and 4x + 3y = 16 →
  34. 34.4x + 9y = 2 and 9x + 4y = 37 →
  35. 35.8x + 2y = 12 and 2x + 8y = −12 →
  36. 36.5x + 2y = −25 and 2x + 3y = 1 →
  37. 37.2x − 3y = −1 and 5x − 4y = 8 →
  38. 38.9x + 7y = −34 and 7x + 9y = −30 →
  39. 39.x + 9y = −22 and 9x + y = 42 →
  40. 40.x + 6y = −9 and 2x + y = 15 →

Answer key

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

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