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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 257 · 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. 1.2x + y = 8 and 2x − 5y = 20 →
  2. 2.5x + 3y = 64 and 3x + 5y = 64 →
  3. 3.3x + 4y = 31 and 4x + 3y = 32 →
  4. 4.6x − 2y = 28 and 2x − 2y = 0 →
  5. 5.3x − 4y = −1 and 2x + y = 14 →
  6. 6.6x + 5y = 0 and x − 6y = −41 →
  7. 7.2x + 4y = −22 and 4x − 6y = 26 →
  8. 8.2x − y = −24 and 3x − 6y = −72 →
  9. 9.2x + 8y = −34 and 8x + 2y = 14 →
  10. 10.4x + 2y = 8 and 2x + 4y = −8 →
  11. 11.5x + 5y = −25 and 3x − 6y = 3 →
  12. 12.x + 5y = 9 and x − y = −9 →
  13. 13.2x + 5y = 34 and 6x + 5y = 62 →
  14. 14.6x + 5y = −2 and x − 3y = 15 →
  15. 15.x + y = 2 and 4x + 5y = 16 →
  16. 16.4x + 3y = 5 and 3x + 4y = −12 →
  17. 17.4x + 2y = 18 and 6x − 2y = −8 →
  18. 18.6x + 4y = −8 and 4x + 6y = −2 →
  19. 19.3x + 5y = 63 and 2x + 6y = 66 →
  20. 20.5x + 4y = 26 and 4x + 6y = 46 →
  21. 21.2x + 8y = 74 and 8x + 2y = 56 →
  22. 22.3x − 2y = 8 and 4x + 2y = 48 →
  23. 23.6x + 4y = −24 and x − 5y = 13 →
  24. 24.4x + y = −37 and 2x + 6y = −68 →
  25. 25.4x + 2y = 4 and 2x + 4y = −22 →
  26. 26.6x + 5y = 17 and 5x + 6y = 27 →
  27. 27.2x + 2y = 10 and 5x + 3y = 11 →
  28. 28.x + 4y = −12 and 4x + y = 12 →
  29. 29.5x + y = −23 and 6x − y = −43 →
  30. 30.x + 5y = 1 and x + 6y = 0 →
  31. 31.2x + 5y = 35 and x − 6y = −25 →
  32. 32.6x + y = 27 and 4x + 6y = 34 →
  33. 33.9x + 2y = 51 and 2x + 9y = 37 →
  34. 34.4x − 6y = −26 and 6x + y = 51 →
  35. 35.3x + 9y = 48 and 9x + 3y = −24 →
  36. 36.x + 3y = −15 and 3x + 4y = −35 →
  37. 37.3x + 4y = 5 and 2x + y = 0 →
  38. 38.x − y = 4 and 2x + 5y = −27 →
  39. 39.x + 5y = 41 and 4x − 4y = −4 →
  40. 40.3x + 3y = 45 and 4x + 3y = 51 →

Answer key

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

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