← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 293 · 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. 1.2x + 4y = 2 and 6x − 5y = 23 →
  2. 2.4x − 4y = 8 and 2x + 3y = 29 →
  3. 3.4x + 2y = 4 and x − 4y = −35 →
  4. 4.7x + 9y = 86 and 9x + 7y = 74 →
  5. 5.x + 2y = 15 and 3x + 3y = 27 →
  6. 6.5x + 6y = 69 and 6x + 5y = 74 →
  7. 7.4x − y = 5 and 2x + 6y = −56 →
  8. 8.4x + 4y = 28 and x − 3y = −13 →
  9. 9.6x + 2y = 42 and 2x − 2y = −2 →
  10. 10.x − 6y = 31 and 6x − 2y = 16 →
  11. 11.3x + 4y = 47 and 3x + 3y = 39 →
  12. 12.x + 9y = −32 and 9x + y = −48 →
  13. 13.2x + 7y = 52 and 7x + 2y = 47 →
  14. 14.3x − 3y = 30 and 4x + 3y = 19 →
  15. 15.3x − 4y = −22 and 4x − 3y = −27 →
  16. 16.3x − 6y = 36 and 2x − 6y = 28 →
  17. 17.7x + 9y = 73 and 9x + 7y = 71 →
  18. 18.5x + 4y = 60 and 4x + 5y = 57 →
  19. 19.3x + 7y = 42 and 7x + 3y = 58 →
  20. 20.x + 2y = 4 and 5x − 3y = 7 →
  21. 21.x + 2y = −4 and 3x + 5y = −11 →
  22. 22.3x − 4y = −1 and 2x + 5y = 7 →
  23. 23.7x + 4y = −22 and 4x + 7y = 11 →
  24. 24.2x + 4y = 0 and 3x − 2y = −32 →
  25. 25.2x − 6y = −38 and x + 4y = 44 →
  26. 26.4x + 4y = −12 and 3x + y = −11 →
  27. 27.x + 6y = 25 and 3x + y = 7 →
  28. 28.6x − 4y = −4 and 4x − 6y = 14 →
  29. 29.5x − 6y = −14 and 6x − 4y = −4 →
  30. 30.7x + 2y = 1 and 2x + 7y = −19 →
  31. 31.5x + 7y = 59 and 7x + 5y = 73 →
  32. 32.5x + 4y = 45 and 6x + y = 35 →
  33. 33.6x + y = −45 and 5x + 5y = 0 →
  34. 34.5x + 5y = 10 and 5x − 2y = −32 →
  35. 35.2x − 5y = −39 and 5x + 5y = 25 →
  36. 36.2x − 3y = −7 and 3x − 3y = −3 →
  37. 37.5x + y = 39 and x + 5y = 3 →
  38. 38.6x + 3y = 51 and 3x + 6y = 30 →
  39. 39.6x − 4y = −46 and x − 4y = −11 →
  40. 40.3x + y = 28 and x + 3y = 12 →

Answer key

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

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