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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 947 · 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. 1.5x + y = 16 and 2x + 6y = 40 →
  2. 2.4x + 5y = −16 and 5x + y = −41 →
  3. 3.x + y = 7 and x − 5y = 13 →
  4. 4.4x − 4y = 24 and 6x − y = 31 →
  5. 5.2x − 5y = 16 and 6x + 5y = 8 →
  6. 6.2x + 2y = −8 and 6x + y = 1 →
  7. 7.2x + 8y = −70 and 8x + 2y = −70 →
  8. 8.x + 2y = 1 and 6x − 6y = 60 →
  9. 9.6x + 4y = 22 and 4x + 6y = 18 →
  10. 10.2x + 5y = −20 and 3x − 2y = −11 →
  11. 11.x + 8y = 74 and 8x + y = 25 →
  12. 12.6x + 3y = 24 and 3x − 2y = −9 →
  13. 13.8x + 5y = 27 and 5x + 8y = 51 →
  14. 14.6x + y = −33 and x + 2y = 11 →
  15. 15.5x − 5y = 10 and 5x + 3y = 26 →
  16. 16.6x + 2y = 18 and 2x − 6y = 46 →
  17. 17.6x + 3y = 12 and 6x + 6y = 6 →
  18. 18.x + 9y = 29 and 9x + y = −59 →
  19. 19.6x + 3y = −3 and 3x + 6y = −15 →
  20. 20.6x + 4y = 2 and 6x + 6y = 18 →
  21. 21.x + y = 15 and 4x − 3y = −3 →
  22. 22.6x + 4y = 26 and 5x − 5y = 80 →
  23. 23.5x + 2y = 6 and 2x + 5y = −6 →
  24. 24.x + 5y = 19 and 5x + y = 47 →
  25. 25.2x + y = 6 and x + 2y = 15 →
  26. 26.x + 2y = 11 and 2x + y = 19 →
  27. 27.6x + 5y = −22 and 5x + 6y = −22 →
  28. 28.6x + 2y = −28 and x + 3y = 6 →
  29. 29.6x + y = 56 and 4x − 2y = 32 →
  30. 30.3x + 3y = 48 and 2x + 3y = 39 →
  31. 31.3x + 9y = 39 and 9x + 3y = 69 →
  32. 32.4x + 7y = −44 and 7x + 4y = −11 →
  33. 33.9x + 6y = 72 and 6x + 9y = 78 →
  34. 34.3x + 5y = 26 and 5x + 3y = 38 →
  35. 35.2x − 4y = 18 and x + 5y = −5 →
  36. 36.2x − 5y = −16 and 3x + y = 10 →
  37. 37.4x + 6y = −8 and x + 5y = 12 →
  38. 38.x + 8y = 57 and 8x + y = 78 →
  39. 39.5x − 4y = −26 and 2x + 3y = 8 →
  40. 40.2x − 2y = −24 and 3x + 3y = −18 →

Answer key

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

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