← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 500 · 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. 1.3x − y = 5 and 2x + 4y = −34 →
  2. 2.4x + 9y = 51 and 9x + 4y = 1 →
  3. 3.3x + y = 11 and x + y = 3 →
  4. 4.3x + 5y = 14 and 6x + 6y = 36 →
  5. 5.5x − y = 30 and 6x + 6y = 72 →
  6. 6.2x + 6y = 20 and 3x − 3y = −18 →
  7. 7.3x + 6y = −6 and 5x + 4y = −16 →
  8. 8.2x + 3y = −22 and 3x + 2y = −28 →
  9. 9.x − y = 6 and x + y = −12 →
  10. 10.6x + y = 53 and 5x + 3y = 55 →
  11. 11.5x + 2y = 19 and 2x + 5y = −5 →
  12. 12.x − 4y = 35 and 2x − 4y = 34 →
  13. 13.4x + 5y = −11 and 2x − 6y = 20 →
  14. 14.9x + 3y = 42 and 3x + 9y = 78 →
  15. 15.5x − 4y = −7 and 6x + 4y = −26 →
  16. 16.6x − 3y = −42 and 5x + 5y = −5 →
  17. 17.3x + 5y = 26 and x + 3y = 10 →
  18. 18.2x + 5y = 14 and 6x + 3y = 18 →
  19. 19.6x + 2y = −40 and 2x + 6y = −40 →
  20. 20.6x + y = 16 and 6x − 6y = 72 →
  21. 21.3x + y = −17 and 2x + 3y = −9 →
  22. 22.2x + 8y = 52 and 8x + 2y = 58 →
  23. 23.2x + 4y = 14 and 4x + 2y = 10 →
  24. 24.5x − 2y = −27 and 3x + 6y = 27 →
  25. 25.5x + 6y = −43 and 6x + 4y = −26 →
  26. 26.x + 2y = 10 and 2x + y = 17 →
  27. 27.8x + 7y = 37 and 7x + 8y = 38 →
  28. 28.3x + 5y = 51 and 5x + 3y = 53 →
  29. 29.6x + 5y = 26 and 5x + 6y = 29 →
  30. 30.2x + 4y = 0 and 4x + 2y = −18 →
  31. 31.4x + 2y = 44 and x + 5y = 47 →
  32. 32.6x + y = 44 and x − y = 5 →
  33. 33.6x + 2y = −36 and 5x + 2y = −32 →
  34. 34.4x − 6y = 42 and 4x + y = 21 →
  35. 35.3x + 4y = 17 and 2x + 6y = 28 →
  36. 36.8x + 2y = −8 and 2x + 8y = −62 →
  37. 37.2x + 3y = 26 and 3x + 2y = 19 →
  38. 38.x − y = −12 and 3x − 6y = −60 →
  39. 39.3x − 2y = 19 and 5x + 2y = −11 →
  40. 40.4x − y = 44 and 3x − 4y = 59 →

Answer key

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

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