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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 135 · 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 − 3y = 29 and 2x − 2y = 22 →
  2. 2.3x − y = 14 and 6x + 2y = 32 →
  3. 3.6x + 2y = 10 and 4x + 6y = 16 →
  4. 4.x − 4y = 0 and x − 5y = −2 →
  5. 5.5x + 2y = 17 and 2x + 5y = −31 →
  6. 6.3x + 2y = 9 and 2x + 6y = 34 →
  7. 7.4x + 3y = 36 and 3x + y = 22 →
  8. 8.6x − 3y = 27 and 4x − 3y = 15 →
  9. 9.4x + 4y = 48 and 2x − 6y = −32 →
  10. 10.9x + 4y = −2 and 4x + 9y = −37 →
  11. 11.x + 3y = 30 and 2x − 6y = −24 →
  12. 12.x + 4y = 10 and 4x − 5y = 19 →
  13. 13.x + 2y = 10 and 4x + 5y = 34 →
  14. 14.5x + 8y = 93 and 8x + 5y = 102 →
  15. 15.9x + 3y = 21 and 3x + 9y = −57 →
  16. 16.2x + y = 15 and 3x + 2y = 24 →
  17. 17.4x + 6y = 22 and x + y = 5 →
  18. 18.6x + 2y = 30 and x − 3y = −25 →
  19. 19.2x − 5y = 49 and 5x + 2y = −8 →
  20. 20.2x + 4y = −4 and 4x + 2y = 16 →
  21. 21.3x + 9y = 33 and 9x + 3y = 51 →
  22. 22.2x + 3y = 19 and 3x + 2y = 16 →
  23. 23.4x + 5y = 36 and 2x − 2y = −18 →
  24. 24.9x + 8y = 88 and 8x + 9y = 82 →
  25. 25.5x + 4y = −24 and x + 2y = −6 →
  26. 26.4x + 3y = 14 and 3x + 4y = 7 →
  27. 27.5x + 4y = −59 and 2x + 5y = −44 →
  28. 28.2x + 6y = −42 and 6x + 2y = 18 →
  29. 29.x + 6y = 44 and 4x + 4y = 36 →
  30. 30.3x + 6y = 21 and 6x + 3y = 24 →
  31. 31.5x + y = −8 and x + 5y = 32 →
  32. 32.4x + 8y = 72 and 8x + 4y = 60 →
  33. 33.x + 4y = 6 and x − 6y = −24 →
  34. 34.x + 4y = 19 and x + y = 7 →
  35. 35.3x + y = −1 and 2x − 5y = −12 →
  36. 36.4x + 2y = −22 and 2x + 4y = −8 →
  37. 37.5x + 2y = 41 and 3x − 5y = 6 →
  38. 38.x − 2y = −20 and 4x − y = −31 →
  39. 39.x + 2y = −15 and 3x − 2y = 19 →
  40. 40.2x − 6y = 46 and 6x − 2y = 58 →

Answer key

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

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