← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 172 · 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. 1.6x + y = 10 and 3x + 6y = 27 →
  2. 2.4x + 3y = 57 and 5x − 2y = 31 →
  3. 3.5x + 4y = 16 and 4x + 5y = 11 →
  4. 4.4x − 4y = 24 and 6x − 5y = 35 →
  5. 5.x − 6y = 37 and 4x + 2y = −8 →
  6. 6.4x + y = −42 and 6x + y = −60 →
  7. 7.x − 6y = 36 and x − 3y = 21 →
  8. 8.5x + 6y = 8 and x − y = 6 →
  9. 9.5x − y = −13 and 2x + 5y = −16 →
  10. 10.5x + 2y = −11 and x + 6y = −47 →
  11. 11.x + 4y = 29 and 3x + y = 21 →
  12. 12.8x + y = −73 and x + 8y = −80 →
  13. 13.x + 4y = 27 and 6x + 6y = 72 →
  14. 14.9x + 6y = 24 and 6x + 9y = 21 →
  15. 15.x + 9y = −55 and 9x + y = 65 →
  16. 16.x + 6y = −46 and 2x + 2y = −12 →
  17. 17.2x − 6y = −6 and 3x + 5y = 33 →
  18. 18.3x + 4y = −1 and 6x + 4y = 2 →
  19. 19.3x + 2y = 5 and 2x + 3y = 5 →
  20. 20.x + y = 4 and 2x − 6y = −40 →
  21. 21.5x + 5y = −25 and 3x + 2y = −9 →
  22. 22.4x − 4y = 32 and x + 6y = 1 →
  23. 23.5x + 2y = 1 and 2x + y = 1 →
  24. 24.2x + y = −16 and 5x + 4y = −43 →
  25. 25.x + y = 9 and 3x + 6y = 48 →
  26. 26.x + 2y = 5 and 4x − y = −16 →
  27. 27.2x + 8y = 74 and 8x + 2y = 86 →
  28. 28.4x + 4y = 20 and 2x + 5y = 19 →
  29. 29.3x + 4y = 25 and 4x + 4y = 28 →
  30. 30.3x + y = 5 and x + 3y = 23 →
  31. 31.6x + 3y = −39 and 2x − 5y = −19 →
  32. 32.2x + 5y = −13 and 5x + 2y = −22 →
  33. 33.4x + y = 22 and x + 3y = 0 →
  34. 34.6x + 6y = 36 and 2x + 6y = 8 →
  35. 35.9x + 8y = −7 and 8x + 9y = −10 →
  36. 36.2x + 2y = −12 and 6x − 5y = −3 →
  37. 37.5x − 6y = 15 and 2x + 3y = 33 →
  38. 38.4x + 6y = −44 and 3x − y = −11 →
  39. 39.3x − 3y = −15 and 6x + 5y = 14 →
  40. 40.5x − y = −32 and x + 2y = −2 →

Answer key

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

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