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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 377 · 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.x − 3y = −15 and 5x + 4y = 39 →
  2. 2.4x + 5y = −31 and 5x + 4y = −41 →
  3. 3.x + 6y = −11 and 3x + 3y = 12 →
  4. 4.x + 3y = 7 and x + 2y = 4 →
  5. 5.4x + 3y = 14 and 3x + 4y = 0 →
  6. 6.2x − 6y = 50 and 5x + 5y = 5 →
  7. 7.5x − 3y = 29 and 2x + 3y = −1 →
  8. 8.x + 5y = −7 and 3x + 3y = 3 →
  9. 9.8x + 6y = 44 and 6x + 8y = 54 →
  10. 10.5x − 2y = 30 and 4x − 5y = 7 →
  11. 11.4x − 3y = 10 and 6x − 4y = 18 →
  12. 12.5x − 2y = −33 and 5x − y = −24 →
  13. 13.4x + 9y = 40 and 9x + 4y = 25 →
  14. 14.6x + y = 26 and x − y = −5 →
  15. 15.3x + 3y = 21 and 2x + y = 9 →
  16. 16.x − 5y = 33 and 5x − 3y = 55 →
  17. 17.4x − 2y = −30 and 6x + 3y = −27 →
  18. 18.2x + 2y = −12 and 2x + y = −4 →
  19. 19.3x + 5y = −12 and 5x + 3y = −4 →
  20. 20.2x + 3y = −16 and 3x + 2y = −19 →
  21. 21.4x − 5y = −2 and x + 6y = −44 →
  22. 22.9x + 2y = 49 and 2x + 9y = 28 →
  23. 23.3x + 4y = 15 and 4x + 3y = 13 →
  24. 24.5x + 5y = 10 and 2x + 3y = −2 →
  25. 25.8x + 2y = 52 and 2x + 8y = 58 →
  26. 26.2x + y = 21 and x + y = 15 →
  27. 27.5x − y = 14 and 6x + 6y = 60 →
  28. 28.3x + 5y = 51 and 6x + 2y = 30 →
  29. 29.5x − 4y = 48 and 2x + y = 1 →
  30. 30.6x − 3y = 15 and 5x + y = −12 →
  31. 31.x − y = 4 and 5x + 6y = −2 →
  32. 32.5x + 2y = 2 and 5x − y = −16 →
  33. 33.5x − 5y = −15 and 4x + y = −22 →
  34. 34.7x + 5y = 28 and 5x + 7y = 44 →
  35. 35.2x − 4y = −8 and 5x + 2y = 28 →
  36. 36.4x − 6y = −34 and 5x − 4y = −25 →
  37. 37.6x + 2y = −14 and 6x + 6y = 6 →
  38. 38.x + y = 1 and 3x + 5y = 1 →
  39. 39.4x + 3y = 1 and 3x + 4y = −1 →
  40. 40.5x + y = 21 and x + 6y = 39 →

Answer key

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

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