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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 727 · 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 + 3y = 39 and 2x − 3y = 9 →
  2. 2.6x + 4y = 6 and 4x − 4y = 44 →
  3. 3.x + 6y = 52 and 2x + 5y = 48 →
  4. 4.5x + 7y = 101 and 7x + 5y = 103 →
  5. 5.5x + 2y = 39 and 2x + y = 16 →
  6. 6.x + 9y = −19 and 9x + y = 69 →
  7. 7.5x + y = −6 and x + 5y = −6 →
  8. 8.5x + 5y = 55 and 4x + 5y = 52 →
  9. 9.2x + 6y = 8 and 4x − 5y = −35 →
  10. 10.3x + 5y = 17 and 3x − 3y = −15 →
  11. 11.5x + y = −18 and x + 5y = 30 →
  12. 12.7x + 9y = 67 and 9x + 7y = 45 →
  13. 13.4x + 9y = −6 and 9x + 4y = 19 →
  14. 14.8x + 4y = 84 and 4x + 8y = 84 →
  15. 15.4x − 4y = −48 and 5x + 2y = 3 →
  16. 16.x + 3y = 3 and 3x + y = 17 →
  17. 17.5x − 4y = 67 and 6x + 6y = −6 →
  18. 18.4x + 3y = 48 and 5x − 2y = 37 →
  19. 19.6x + 7y = −3 and 7x + 6y = −10 →
  20. 20.2x − y = 7 and 2x − 5y = −13 →
  21. 21.5x + 6y = 17 and 6x + 6y = 12 →
  22. 22.3x + 3y = 6 and 3x + 4y = 1 →
  23. 23.4x − 3y = −23 and 4x + 3y = −41 →
  24. 24.9x + 6y = −51 and 6x + 9y = −54 →
  25. 25.9x + 6y = −24 and 6x + 9y = 9 →
  26. 26.4x + 4y = 24 and 6x − 6y = 60 →
  27. 27.2x + 2y = 26 and 5x − y = 41 →
  28. 28.4x + 3y = −53 and x − 3y = 13 →
  29. 29.2x + 4y = 34 and 4x + 2y = 14 →
  30. 30.3x + 6y = 33 and 5x − 6y = −41 →
  31. 31.4x + 4y = 44 and 4x + 5y = 46 →
  32. 32.2x + 3y = 21 and 3x + 2y = 24 →
  33. 33.4x − y = 25 and 6x + 3y = −3 →
  34. 34.x + 4y = −19 and 5x − 6y = 61 →
  35. 35.2x + 2y = 32 and 4x + 3y = 55 →
  36. 36.6x + 4y = 66 and 3x + 4y = 39 →
  37. 37.2x + 5y = 24 and 3x + y = 23 →
  38. 38.8x + 3y = 15 and 3x + 8y = −15 →
  39. 39.5x + 3y = 28 and 3x + 3y = 24 →
  40. 40.2x + 8y = −6 and 8x + 2y = 6 →

Answer key

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

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