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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 692 · 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 + 5y = 9 and 5x + 6y = 13 →
  2. 2.x + 5y = 24 and 6x − y = 20 →
  3. 3.2x + 5y = −6 and 5x + 4y = 19 →
  4. 4.6x + 7y = 19 and 7x + 6y = 20 →
  5. 5.5x − 2y = −13 and 6x − 6y = −48 →
  6. 6.4x + 7y = 36 and 7x + 4y = 30 →
  7. 7.4x + 5y = −48 and 5x − 3y = 14 →
  8. 8.5x + 6y = 82 and 5x + y = 47 →
  9. 9.3x + 2y = 11 and 2x − y = 26 →
  10. 10.4x − 3y = 27 and x − 3y = 0 →
  11. 11.5x − 2y = 52 and 5x + y = 34 →
  12. 12.x + 4y = 19 and 4x + y = 16 →
  13. 13.4x − 2y = −34 and 5x + y = −39 →
  14. 14.4x + 3y = 21 and 6x − 5y = 79 →
  15. 15.5x + 9y = −22 and 9x + 5y = −6 →
  16. 16.6x + 6y = −6 and 2x − 3y = 18 →
  17. 17.5x + 2y = 36 and 2x − 4y = −24 →
  18. 18.3x + 2y = −31 and 6x + 3y = −57 →
  19. 19.6x + 5y = −76 and 6x + 6y = −84 →
  20. 20.4x + 2y = 6 and 3x + 4y = −8 →
  21. 21.x + 4y = 16 and 6x + 3y = −9 →
  22. 22.9x + 6y = 105 and 6x + 9y = 105 →
  23. 23.8x + 6y = 6 and 6x + 8y = 36 →
  24. 24.4x + 2y = 22 and 2x + 4y = 14 →
  25. 25.5x − y = 29 and 5x − 2y = 23 →
  26. 26.5x + 8y = −92 and 8x + 5y = −77 →
  27. 27.2x − 3y = 1 and 4x + 2y = 10 →
  28. 28.8x + 6y = −40 and 6x + 8y = −44 →
  29. 29.6x + 5y = 26 and 2x + 5y = 2 →
  30. 30.5x + 3y = 69 and 3x + 5y = 67 →
  31. 31.2x − 3y = −12 and 4x + y = 32 →
  32. 32.6x − 3y = −57 and x + 2y = −2 →
  33. 33.5x + y = −29 and x + 3y = −17 →
  34. 34.3x − 6y = −24 and 4x + 6y = 66 →
  35. 35.2x + 3y = 1 and x − 4y = 17 →
  36. 36.2x + 3y = −2 and 5x − 6y = −59 →
  37. 37.x + y = −4 and x + 6y = 1 →
  38. 38.5x + y = −16 and x + 5y = 40 →
  39. 39.4x − 2y = 8 and 6x + 6y = 30 →
  40. 40.x + 5y = −21 and 6x + 5y = −26 →

Answer key

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

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