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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 68 · 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 + 3y = −10 and 3x + 4y = 3 →
  2. 2.5x + 9y = −107 and 9x + 5y = −103 →
  3. 3.3x − 5y = −31 and x − 6y = −32 →
  4. 4.5x + 2y = −11 and 2x + 5y = 25 →
  5. 5.2x + y = 10 and 6x + 5y = 34 →
  6. 6.9x + 5y = −77 and 5x + 9y = −49 →
  7. 7.3x + 4y = 14 and 2x − 2y = 0 →
  8. 8.x + 2y = 23 and 2x + 5y = 55 →
  9. 9.5x − y = 11 and 5x + y = −1 →
  10. 10.6x + 4y = −4 and 4x + 6y = 4 →
  11. 11.2x + 3y = −24 and 3x + 4y = −35 →
  12. 12.x + 5y = 11 and 4x + 3y = 27 →
  13. 13.6x + 6y = 36 and 5x + 2y = 6 →
  14. 14.4x − y = 3 and 2x + 2y = 24 →
  15. 15.2x + 2y = 24 and 4x + 2y = 40 →
  16. 16.8x + y = 14 and x + 8y = −14 →
  17. 17.2x − 2y = −8 and 2x + 6y = 0 →
  18. 18.2x + 7y = 51 and 7x + 2y = 21 →
  19. 19.5x + 6y = 74 and 5x + y = 29 →
  20. 20.8x + 9y = −5 and 9x + 8y = −12 →
  21. 21.3x − 4y = −34 and 6x + 2y = −28 →
  22. 22.5x + 2y = 61 and 2x + 5y = 58 →
  23. 23.2x − 4y = −10 and 6x + 6y = 96 →
  24. 24.6x − 6y = 72 and x − 4y = 36 →
  25. 25.3x + 9y = 9 and 9x + 3y = 51 →
  26. 26.x + 2y = −4 and x − 2y = −8 →
  27. 27.5x + 3y = 14 and 3x − y = 14 →
  28. 28.4x + y = 27 and x + 2y = 19 →
  29. 29.4x + 6y = −24 and 6x + 4y = −26 →
  30. 30.6x − 6y = −96 and 6x + 5y = −8 →
  31. 31.x + 6y = 57 and 3x + 4y = 45 →
  32. 32.8x + 5y = 13 and 5x + 8y = 13 →
  33. 33.6x + 5y = 72 and 5x + 6y = 71 →
  34. 34.3x − y = −7 and 2x − y = −5 →
  35. 35.x + 6y = −9 and 6x + y = 16 →
  36. 36.2x + 2y = 24 and 4x + 2y = 30 →
  37. 37.x + y = 6 and x + 2y = 7 →
  38. 38.6x + y = 28 and 2x + 4y = 2 →
  39. 39.x − 2y = 8 and x + 5y = −34 →
  40. 40.4x + 6y = −58 and 6x + 4y = −62 →

Answer key

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

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