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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 331 · 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 = 7 and 5x + y = 6 →
  2. 2.3x + y = 7 and 5x + 2y = 12 →
  3. 3.x + 3y = 4 and 6x − y = 5 →
  4. 4.3x + 4y = −29 and 3x + 6y = −39 →
  5. 5.6x + 2y = 8 and 4x − 2y = −18 →
  6. 6.3x + 3y = 0 and x + 2y = 7 →
  7. 7.6x + 6y = 6 and 2x + 6y = −6 →
  8. 8.2x + y = 10 and 3x + y = 12 →
  9. 9.6x + 2y = −24 and 4x + y = −18 →
  10. 10.2x + 3y = 21 and 3x + 2y = 29 →
  11. 11.4x + y = −3 and x + 2y = −13 →
  12. 12.4x + 3y = −29 and 4x + 2y = −26 →
  13. 13.6x − 3y = 21 and 6x − 5y = 19 →
  14. 14.4x − 5y = −3 and 3x − y = 6 →
  15. 15.3x − 5y = 5 and 3x + y = 17 →
  16. 16.2x − y = 8 and 4x + 5y = 2 →
  17. 17.2x − y = 11 and 3x − 6y = 3 →
  18. 18.4x + 8y = 44 and 8x + 4y = 16 →
  19. 19.6x − 4y = −18 and 6x − 3y = −15 →
  20. 20.6x + y = 57 and 5x + 2y = 51 →
  21. 21.2x + 5y = −49 and 3x + y = −15 →
  22. 22.4x + 2y = 22 and 2x + 4y = −4 →
  23. 23.x + 6y = 56 and x + 4y = 38 →
  24. 24.8x + 9y = 29 and 9x + 8y = 22 →
  25. 25.2x + 3y = −16 and 3x + 2y = −4 →
  26. 26.9x + 6y = 6 and 6x + 9y = 39 →
  27. 27.4x + 5y = 7 and 3x + 4y = 5 →
  28. 28.x + 5y = 11 and x − y = −13 →
  29. 29.3x + 7y = −78 and 7x + 3y = −62 →
  30. 30.6x − 2y = 50 and 6x − 4y = 46 →
  31. 31.4x + 4y = −48 and 6x + 5y = −69 →
  32. 32.x − 6y = 35 and x + y = −14 →
  33. 33.3x − 3y = −12 and 5x − 6y = −29 →
  34. 34.6x + 4y = −20 and 6x − y = 20 →
  35. 35.6x + 4y = 44 and 4x + 6y = 46 →
  36. 36.9x + 8y = −32 and 8x + 9y = −19 →
  37. 37.7x + 3y = −7 and 3x + 7y = −43 →
  38. 38.2x + 2y = −6 and 4x − 4y = −20 →
  39. 39.4x − 3y = −16 and 5x + y = 18 →
  40. 40.2x + 6y = −20 and 5x − 2y = 18 →

Answer key

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

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