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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 381 · 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 + 4y = 48 and 6x + y = 56 →
  2. 2.4x − 6y = −56 and 4x − 2y = −24 →
  3. 3.2x + 8y = 36 and 8x + 2y = −36 →
  4. 4.2x + 7y = −11 and 7x + 2y = 29 →
  5. 5.6x + y = 22 and 6x − y = 38 →
  6. 6.7x + 6y = 31 and 6x + 7y = 34 →
  7. 7.5x + 2y = 38 and 3x − 3y = 27 →
  8. 8.6x + 3y = 69 and 3x − 2y = 17 →
  9. 9.4x + 5y = 4 and 5x + 4y = −4 →
  10. 10.2x + y = 10 and x − 2y = 0 →
  11. 11.2x + 5y = −29 and 5x + 2y = −41 →
  12. 12.2x + y = 20 and x + 2y = 22 →
  13. 13.3x − 6y = 48 and 4x + 5y = −14 →
  14. 14.2x + 3y = 2 and 2x + y = −6 →
  15. 15.5x + 4y = −3 and 6x − 2y = −58 →
  16. 16.2x + 3y = 5 and x + y = 2 →
  17. 17.6x + 5y = −29 and 5x − 2y = −55 →
  18. 18.x + 2y = −17 and x + 5y = −41 →
  19. 19.x + 2y = −15 and x − 5y = 41 →
  20. 20.3x + 5y = 19 and 5x + 3y = 5 →
  21. 21.5x + 2y = 5 and 4x − 6y = 42 →
  22. 22.4x + 8y = 36 and 8x + 4y = 48 →
  23. 23.x + 8y = 34 and 8x + y = 20 →
  24. 24.5x + 7y = 48 and 7x + 5y = 48 →
  25. 25.x + 3y = 11 and 4x − y = 5 →
  26. 26.4x + 5y = −2 and 5x − 6y = 71 →
  27. 27.4x + 2y = 2 and 2x − 5y = −17 →
  28. 28.5x + 2y = −15 and 2x + 5y = 15 →
  29. 29.3x + y = 12 and 2x + 5y = 47 →
  30. 30.x + 3y = −25 and 3x + y = −3 →
  31. 31.2x − 3y = 11 and 3x + 4y = 25 →
  32. 32.2x + 6y = −44 and 2x − 2y = 4 →
  33. 33.7x + 2y = 67 and 2x + 7y = 32 →
  34. 34.x − 3y = −8 and 4x − y = 1 →
  35. 35.3x − 5y = −8 and 2x + 2y = −16 →
  36. 36.6x + 6y = −6 and 3x + 2y = −6 →
  37. 37.2x + 2y = 32 and x − y = 2 →
  38. 38.x + 6y = 41 and 6x + y = 1 →
  39. 39.2x + y = −16 and 6x + 6y = −54 →
  40. 40.2x − 6y = −44 and x − 2y = −15 →

Answer key

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

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