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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 672 · 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 − 6y = 62 and x + 3y = −25 →
  2. 2.4x + 5y = 21 and 3x + 2y = 21 →
  3. 3.2x + 4y = 2 and 4x + 2y = 16 →
  4. 4.3x − 4y = 23 and 4x + 6y = 42 →
  5. 5.x − 3y = −16 and 2x − 3y = −11 →
  6. 6.x − 4y = 15 and 6x + 5y = 3 →
  7. 7.4x − 5y = 33 and 6x + 6y = 36 →
  8. 8.2x + 7y = 77 and 7x + 2y = 67 →
  9. 9.x − 2y = −12 and 6x + y = −46 →
  10. 10.2x + y = 15 and 2x + 6y = 10 →
  11. 11.x + 5y = 30 and 2x − 2y = 0 →
  12. 12.6x + 6y = 54 and x − 2y = −9 →
  13. 13.3x + y = 3 and 3x + 5y = 39 →
  14. 14.2x + 4y = 42 and 2x + 6y = 58 →
  15. 15.5x + 4y = −36 and 4x + 5y = −27 →
  16. 16.5x + 5y = −35 and 6x − 5y = −9 →
  17. 17.x + 3y = −1 and 3x + y = −11 →
  18. 18.6x + 4y = 26 and 4x + 6y = 34 →
  19. 19.6x + 5y = 68 and 3x − y = 20 →
  20. 20.2x + 3y = 4 and 3x − 4y = 40 →
  21. 21.5x − 5y = −35 and 5x + 5y = −45 →
  22. 22.6x + y = −8 and 5x − 5y = −30 →
  23. 23.6x − 4y = −48 and 2x + 2y = 4 →
  24. 24.3x − 5y = −2 and x + 2y = −8 →
  25. 25.2x + 8y = −54 and 8x + 2y = 24 →
  26. 26.6x + 6y = 36 and 5x + 2y = 21 →
  27. 27.5x + 6y = −23 and x − 2y = 5 →
  28. 28.6x + 3y = 48 and 3x + 6y = 51 →
  29. 29.6x + 8y = 2 and 8x + 6y = 12 →
  30. 30.5x − y = 18 and 2x + 2y = 12 →
  31. 31.9x + 4y = −39 and 4x + 9y = 26 →
  32. 32.5x + 2y = −51 and 2x + 5y = −54 →
  33. 33.2x + 3y = 31 and 3x + 5y = 49 →
  34. 34.4x + 2y = 28 and 2x + 4y = 26 →
  35. 35.9x + 3y = 78 and 3x + 9y = 42 →
  36. 36.4x − 5y = −49 and x + y = 8 →
  37. 37.6x + 2y = 60 and 5x + y = 48 →
  38. 38.x + 5y = −27 and x − 2y = 15 →
  39. 39.x + 8y = −15 and 8x + y = −57 →
  40. 40.7x + 5y = 5 and 5x + 7y = −17 →

Answer key

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

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