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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 422 · 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 = 12 and 4x − 3y = 14 →
  2. 2.4x − 4y = 16 and 4x − 6y = 14 →
  3. 3.x − 2y = −5 and 2x − 2y = 0 →
  4. 4.7x + 2y = −12 and 2x + 7y = 3 →
  5. 5.4x + 5y = 18 and x + 5y = 27 →
  6. 6.5x + y = 16 and 2x + y = 1 →
  7. 7.x + 7y = 4 and 7x + y = −20 →
  8. 8.3x + 8y = 75 and 8x + 3y = 35 →
  9. 9.7x + 6y = −15 and 6x + 7y = −24 →
  10. 10.5x + 3y = −1 and 3x + 5y = −7 →
  11. 11.9x + 6y = 54 and 6x + 9y = 66 →
  12. 12.2x + 5y = −23 and 5x + 2y = −47 →
  13. 13.9x + 6y = −39 and 6x + 9y = −6 →
  14. 14.x − 4y = −37 and 4x + 5y = 20 →
  15. 15.6x + 6y = 60 and 5x − 2y = 8 →
  16. 16.5x + y = −29 and 2x − y = −20 →
  17. 17.3x + 7y = −4 and 7x + 3y = 4 →
  18. 18.3x + 4y = −20 and 4x + 3y = −29 →
  19. 19.2x − 6y = −54 and x + 2y = 3 →
  20. 20.3x + 5y = −13 and 5x + y = −7 →
  21. 21.7x + 6y = 26 and 6x + 7y = 13 →
  22. 22.5x + 3y = 8 and 4x + 2y = 6 →
  23. 23.6x + 2y = −22 and 2x + 6y = −50 →
  24. 24.4x − y = 9 and 6x + 6y = 6 →
  25. 25.5x − 2y = 13 and 5x − 5y = 10 →
  26. 26.2x + 4y = 22 and 2x + 6y = 40 →
  27. 27.2x + y = −8 and 6x + 6y = −42 →
  28. 28.x + y = −7 and 5x + 2y = −41 →
  29. 29.x + 5y = 22 and 5x + y = 14 →
  30. 30.7x + 3y = 32 and 3x + 7y = 48 →
  31. 31.2x + y = −26 and x + 2y = −25 →
  32. 32.5x + y = 43 and x + 5y = 47 →
  33. 33.4x − 2y = −10 and x − y = −6 →
  34. 34.6x + y = 1 and x + 6y = 41 →
  35. 35.8x + 4y = 76 and 4x + 8y = 56 →
  36. 36.4x + 6y = 22 and 6x + 4y = 38 →
  37. 37.6x + 6y = −12 and 6x − 4y = −72 →
  38. 38.7x + 9y = −55 and 9x + 7y = −57 →
  39. 39.5x − 5y = −20 and 3x + 6y = −39 →
  40. 40.5x + 9y = 83 and 9x + 5y = 71 →

Answer key

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

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