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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 301 · 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 + y = 14 and x + 4y = 26 →
  2. 2.4x + 5y = 65 and 5x + 4y = 61 →
  3. 3.x + 4y = −9 and 4x − 2y = 36 →
  4. 4.4x + 7y = 67 and 7x + 4y = 43 →
  5. 5.2x + 5y = 36 and 5x + 2y = 48 →
  6. 6.5x + 6y = 5 and 5x − 4y = 55 →
  7. 7.5x + 3y = 49 and 4x + 5y = 60 →
  8. 8.6x + 7y = −62 and 7x + 6y = −55 →
  9. 9.x + 6y = 21 and 6x + 5y = 33 →
  10. 10.2x + 4y = 34 and 6x + y = 47 →
  11. 11.5x + 4y = −17 and 4x + y = −18 →
  12. 12.x − 2y = −5 and 3x + 2y = −7 →
  13. 13.6x + 5y = −6 and 5x + 6y = −16 →
  14. 14.2x + 2y = −18 and 5x − 5y = 25 →
  15. 15.6x − y = −31 and 2x + 3y = 13 →
  16. 16.6x + 3y = 3 and 3x − 4y = −15 →
  17. 17.7x + y = −58 and x + 7y = 26 →
  18. 18.4x + 6y = 30 and 5x − y = −22 →
  19. 19.5x + 5y = 80 and 5x + 4y = 71 →
  20. 20.4x + 4y = 0 and 5x + 2y = 12 →
  21. 21.5x + 6y = 47 and 6x + 5y = 52 →
  22. 22.x + 4y = 37 and 4x + y = 28 →
  23. 23.2x + 8y = 42 and 8x + 2y = 78 →
  24. 24.5x + 3y = 16 and 3x + 5y = 16 →
  25. 25.5x − y = −9 and 4x + 2y = 4 →
  26. 26.3x + 3y = −36 and 6x + 4y = −64 →
  27. 27.5x + 6y = 3 and 6x + 5y = −3 →
  28. 28.5x + 5y = 15 and 4x + 3y = 10 →
  29. 29.5x + y = 16 and x − 4y = 20 →
  30. 30.6x + y = 11 and x + 6y = 31 →
  31. 31.6x + 5y = −14 and 3x + 2y = −5 →
  32. 32.x + 8y = −39 and 8x + y = 3 →
  33. 33.2x + 5y = −19 and 2x − 2y = 30 →
  34. 34.3x + 9y = −24 and 9x + 3y = 48 →
  35. 35.2x + y = 0 and x + 2y = −3 →
  36. 36.6x + y = −35 and x + 6y = −35 →
  37. 37.3x + 5y = 46 and 5x + 3y = 50 →
  38. 38.2x + 4y = 38 and 4x + 6y = 62 →
  39. 39.5x + 3y = −31 and 2x − 3y = −25 →
  40. 40.x − 3y = 31 and 3x + 3y = −15 →

Answer key

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

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