← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 648 · 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. 1.7x + 4y = 15 and 4x + 7y = 18 →
  2. 2.2x + 4y = 46 and 4x + 2y = 38 →
  3. 3.6x + 2y = 0 and 2x + 6y = −32 →
  4. 4.3x + 5y = 0 and 5x + 3y = −16 →
  5. 5.3x + 4y = −6 and 2x + y = 6 →
  6. 6.6x + 5y = 40 and 3x − 2y = 11 →
  7. 7.3x + 9y = −3 and 9x + 3y = 39 →
  8. 8.7x + 2y = −81 and 2x + 7y = −81 →
  9. 9.3x − y = −4 and 4x + 5y = −37 →
  10. 10.3x − y = 7 and 6x + y = 20 →
  11. 11.8x + 2y = 72 and 2x + 8y = 48 →
  12. 12.5x + 2y = 15 and 4x + 2y = 14 →
  13. 13.6x + 3y = 15 and x + 2y = 7 →
  14. 14.3x + 2y = 34 and 2x + 3y = 31 →
  15. 15.6x + 2y = 28 and 2x + 6y = 36 →
  16. 16.x + 2y = 1 and 6x + y = 17 →
  17. 17.5x − 5y = 10 and 3x + y = 2 →
  18. 18.x + 9y = 15 and 9x + y = 55 →
  19. 19.4x + y = 31 and x + 4y = 4 →
  20. 20.5x − y = 18 and 4x − 2y = 18 →
  21. 21.4x + 3y = 49 and 3x + 4y = 49 →
  22. 22.8x + 4y = 8 and 4x + 8y = −8 →
  23. 23.9x + 8y = −137 and 8x + 9y = −135 →
  24. 24.3x − y = 7 and x − 5y = −21 →
  25. 25.2x + 5y = 56 and 5x + 2y = 56 →
  26. 26.2x + 4y = 20 and 4x − 2y = 10 →
  27. 27.3x + 8y = 1 and 8x + 3y = 21 →
  28. 28.6x + 3y = 21 and 3x + 6y = 15 →
  29. 29.3x + 2y = 35 and 5x + 3y = 57 →
  30. 30.3x + 7y = 49 and 7x + 3y = 61 →
  31. 31.x + 6y = −28 and 5x + 2y = 28 →
  32. 32.x − 6y = −63 and 5x + y = −36 →
  33. 33.6x + y = −60 and x − y = −3 →
  34. 34.7x + 4y = 43 and 4x + 7y = 1 →
  35. 35.x + y = 16 and 4x − 4y = 0 →
  36. 36.3x + y = 32 and 4x + 5y = 61 →
  37. 37.6x + 8y = −100 and 8x + 6y = −96 →
  38. 38.6x − 3y = −48 and 3x + 3y = −33 →
  39. 39.4x − 5y = 1 and 4x − 2y = 22 →
  40. 40.x + 2y = −20 and 6x + y = −21 →

Answer key

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

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