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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 871 · 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 − 2y = −16 and x + 4y = −31 →
  2. 2.5x + 6y = 53 and x + y = 10 →
  3. 3.4x + 2y = −44 and 2x + 4y = −34 →
  4. 4.2x − y = 7 and 3x + 3y = 51 →
  5. 5.3x − y = 4 and x + 6y = −5 →
  6. 6.2x + 5y = 36 and 5x − 2y = 32 →
  7. 7.x + 6y = 15 and 4x − y = 10 →
  8. 8.5x + y = 16 and x + 5y = 32 →
  9. 9.3x − y = 18 and 3x − 2y = 15 →
  10. 10.9x + 4y = 21 and 4x + 9y = −34 →
  11. 11.9x + 7y = 103 and 7x + 9y = 105 →
  12. 12.3x + 2y = 23 and 2x + 3y = 27 →
  13. 13.7x + 4y = 13 and 4x + 7y = 31 →
  14. 14.7x + 6y = −21 and 6x + 7y = −5 →
  15. 15.5x − 2y = −9 and 4x + 4y = 32 →
  16. 16.2x − y = 8 and 6x + 3y = 12 →
  17. 17.3x + 5y = −14 and 5x + 3y = −34 →
  18. 18.2x + 5y = −7 and 2x + 6y = −12 →
  19. 19.6x + y = −4 and 3x − 3y = −9 →
  20. 20.2x − 4y = 6 and 4x + 2y = −28 →
  21. 21.x + 6y = 24 and 5x − 5y = 15 →
  22. 22.9x + 8y = 86 and 8x + 9y = 84 →
  23. 23.6x + 8y = 82 and 8x + 6y = 72 →
  24. 24.5x + 3y = 32 and x − 3y = −26 →
  25. 25.5x + 5y = −25 and 6x − 5y = 14 →
  26. 26.2x + 5y = 24 and x + y = 6 →
  27. 27.2x + 6y = 30 and 2x + 4y = 24 →
  28. 28.6x + 3y = 24 and 3x + 6y = 21 →
  29. 29.2x + 5y = 25 and x + 3y = 16 →
  30. 30.2x + 5y = −26 and x − 5y = 47 →
  31. 31.7x + 3y = 74 and 3x + 7y = 66 →
  32. 32.2x − 3y = −4 and x + 2y = 12 →
  33. 33.x + 6y = 10 and 6x + 4y = 28 →
  34. 34.x + 3y = −6 and 6x + 4y = −22 →
  35. 35.x + 3y = −7 and 3x + y = 3 →
  36. 36.4x + 5y = 22 and 5x + 2y = 19 →
  37. 37.5x + 5y = 15 and 2x + 4y = 10 →
  38. 38.6x + 3y = 33 and x − y = −2 →
  39. 39.3x + y = 16 and x + 4y = −13 →
  40. 40.8x + 5y = 92 and 5x + 8y = 77 →

Answer key

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

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