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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 275 · 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. 1.5x + 2y = −20 and 6x − y = −41 →
  2. 2.5x + 4y = −22 and 3x + 3y = −12 →
  3. 3.6x + 4y = −82 and 2x + 2y = −32 →
  4. 4.6x + 2y = −40 and 2x + 6y = −24 →
  5. 5.5x + 5y = 10 and x − 2y = 5 →
  6. 6.x + 9y = 39 and 9x + y = 31 →
  7. 7.3x + 6y = 36 and 4x + 2y = 6 →
  8. 8.2x + 2y = 18 and 6x − 3y = −9 →
  9. 9.2x + 6y = 60 and 6x + 2y = 36 →
  10. 10.2x + 4y = 26 and 5x − 6y = 33 →
  11. 11.3x + 6y = −12 and 5x + 3y = −27 →
  12. 12.2x + 5y = 36 and 5x + 2y = 48 →
  13. 13.8x + 2y = −82 and 2x + 8y = −88 →
  14. 14.6x + 3y = 57 and 4x + 5y = 47 →
  15. 15.5x − 3y = 18 and 4x + 3y = 63 →
  16. 16.6x + 7y = −23 and 7x + 6y = −29 →
  17. 17.5x − 2y = −38 and 3x − 2y = −22 →
  18. 18.x + 2y = 9 and 3x + 4y = 17 →
  19. 19.6x + 2y = 34 and 6x − y = 37 →
  20. 20.x + 3y = 25 and 3x + y = 11 →
  21. 21.3x + 6y = 42 and 4x + y = 21 →
  22. 22.4x + 3y = 28 and 3x − 2y = −13 →
  23. 23.x + 9y = −13 and 9x + y = 43 →
  24. 24.5x + 9y = −107 and 9x + 5y = −103 →
  25. 25.5x − 4y = −13 and 6x + 4y = 46 →
  26. 26.x − 4y = −29 and 6x + 5y = 87 →
  27. 27.6x − 5y = 49 and 2x − 5y = 33 →
  28. 28.2x + y = 14 and 6x + 6y = 48 →
  29. 29.x − y = −1 and 2x + y = 22 →
  30. 30.4x + 4y = 0 and 2x − 2y = −24 →
  31. 31.2x + y = 2 and x + 2y = −2 →
  32. 32.5x − 2y = 31 and 4x + 3y = 34 →
  33. 33.x + 5y = −34 and 3x − 3y = 42 →
  34. 34.7x + 9y = −58 and 9x + 7y = −70 →
  35. 35.3x + 2y = 25 and 2x + 3y = 20 →
  36. 36.2x + 3y = 4 and 3x + 2y = 11 →
  37. 37.4x + y = 31 and 2x + 3y = 23 →
  38. 38.3x − y = 4 and 5x + 3y = −26 →
  39. 39.9x + 3y = −57 and 3x + 9y = 45 →
  40. 40.5x − 4y = −15 and x + y = 6 →

Answer key

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

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