← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 706 · 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. 1.4x + 2y = 26 and 2x + 4y = 10 →
  2. 2.x − 3y = 18 and 2x + 5y = −19 →
  3. 3.8x + 6y = −10 and 6x + 8y = 24 →
  4. 4.5x + y = 16 and x + 5y = 8 →
  5. 5.3x + 8y = 20 and 8x + 3y = 35 →
  6. 6.6x + 2y = 56 and 2x + 6y = 40 →
  7. 7.3x + 4y = −41 and 4x + 3y = −36 →
  8. 8.5x + 8y = 18 and 8x + 5y = 21 →
  9. 9.x − 3y = 31 and 4x + 2y = 12 →
  10. 10.x + 5y = 42 and 3x − 6y = −63 →
  11. 11.2x − 3y = 9 and 3x − 4y = 15 →
  12. 12.6x + y = 60 and x − y = 3 →
  13. 13.5x + 5y = 20 and 5x + y = 12 →
  14. 14.6x + 3y = 12 and x − y = −1 →
  15. 15.6x − y = 45 and 4x + 2y = 22 →
  16. 16.3x + 2y = −7 and 2x + 3y = 7 →
  17. 17.x − 5y = −37 and x − y = −13 →
  18. 18.4x + y = 27 and 4x + 5y = 39 →
  19. 19.3x + 6y = 15 and 6x + 3y = 21 →
  20. 20.3x − y = 12 and 6x + 4y = 42 →
  21. 21.x + 2y = −9 and 2x + y = 0 →
  22. 22.2x + 2y = −4 and 3x + 4y = −13 →
  23. 23.5x − 2y = 6 and x + 4y = 32 →
  24. 24.6x − 3y = 63 and 6x − 4y = 68 →
  25. 25.x − 4y = 33 and 2x + 3y = −22 →
  26. 26.3x − 3y = −6 and x − 4y = −11 →
  27. 27.6x + 5y = 83 and 2x − 6y = −26 →
  28. 28.x − 6y = −21 and 5x + 4y = 65 →
  29. 29.2x + 3y = 21 and 3x + 2y = 19 →
  30. 30.2x − 5y = −28 and 6x + 2y = 18 →
  31. 31.6x − 3y = −3 and x − 5y = −23 →
  32. 32.4x − 6y = 2 and 5x + 3y = 13 →
  33. 33.6x + 9y = −57 and 9x + 6y = −18 →
  34. 34.5x + 3y = −11 and 3x − 4y = −53 →
  35. 35.4x + 4y = 16 and 4x − y = 31 →
  36. 36.5x + y = 2 and 2x − 5y = 44 →
  37. 37.2x + y = −8 and x + 2y = 2 →
  38. 38.6x + 2y = −32 and 2x + 6y = 16 →
  39. 39.3x + 2y = 26 and 2x + 3y = 19 →
  40. 40.x + 8y = −10 and 8x + y = −17 →

Answer key

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

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