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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 883 · 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 + 4y = −10 and 6x + 3y = −15 →
  2. 2.5x + 2y = 41 and 2x + 5y = 8 →
  3. 3.2x + 5y = 43 and x + y = 14 →
  4. 4.3x + y = 4 and 2x − 3y = 10 →
  5. 5.x + y = −15 and 4x − 5y = 21 →
  6. 6.x − 4y = −2 and 5x − 3y = 7 →
  7. 7.7x + 2y = 60 and 2x + 7y = 30 →
  8. 8.2x + 5y = −28 and 4x − 5y = 4 →
  9. 9.4x + y = 7 and x − 5y = 49 →
  10. 10.2x − y = 10 and 2x + 2y = 28 →
  11. 11.x + 9y = 47 and 9x + y = −57 →
  12. 12.4x + 8y = −48 and 8x + 4y = 12 →
  13. 13.x − 6y = 49 and 2x − 2y = 18 →
  14. 14.x + 3y = −22 and 6x + 4y = −48 →
  15. 15.3x + 9y = 24 and 9x + 3y = −24 →
  16. 16.2x + 6y = −14 and 2x + 5y = −13 →
  17. 17.2x + y = −3 and x − y = −3 →
  18. 18.5x + 2y = −6 and 2x + y = −4 →
  19. 19.4x − y = −16 and x + 2y = 5 →
  20. 20.6x + 4y = 70 and 4x + 5y = 56 →
  21. 21.2x − 4y = −6 and 6x + y = 8 →
  22. 22.4x + 6y = 14 and 5x − 3y = 49 →
  23. 23.4x + y = −31 and 3x + 5y = −19 →
  24. 24.3x − 5y = −48 and 3x + 5y = 12 →
  25. 25.6x + 6y = −24 and 4x + 3y = −20 →
  26. 26.x + 4y = 44 and 4x + y = 41 →
  27. 27.9x + 4y = 117 and 4x + 9y = 117 →
  28. 28.3x + y = 31 and 2x + y = 23 →
  29. 29.9x + 7y = −4 and 7x + 9y = −28 →
  30. 30.2x + 6y = 60 and 5x − 2y = 14 →
  31. 31.x + 8y = 58 and 8x + y = −40 →
  32. 32.4x + 5y = 7 and 5x + 4y = 20 →
  33. 33.3x + 3y = −15 and 5x + y = −29 →
  34. 34.6x + 7y = 19 and 7x + 6y = 20 →
  35. 35.x + y = 7 and 3x − 3y = 9 →
  36. 36.6x − 4y = −52 and 5x + y = −26 →
  37. 37.3x + 5y = −62 and 5x + 3y = −66 →
  38. 38.6x + 8y = 78 and 8x + 6y = 76 →
  39. 39.x + 4y = 7 and x + 6y = 9 →
  40. 40.3x + 2y = −8 and 5x − y = −48 →

Answer key

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

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