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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 677 · 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. 1.6x + 3y = 27 and 3x + 6y = 27 →
  2. 2.5x + 5y = 20 and 2x + y = −1 →
  3. 3.2x + 6y = 36 and 2x − 2y = −4 →
  4. 4.6x − 4y = 38 and x + 6y = 13 →
  5. 5.8x + 3y = 13 and 3x + 8y = −57 →
  6. 6.x − y = 3 and 5x − y = 35 →
  7. 7.2x + 6y = 36 and 3x + y = 22 →
  8. 8.4x + y = 41 and x + 4y = 44 →
  9. 9.x + 3y = 31 and 3x + y = 21 →
  10. 10.2x + 9y = −71 and 9x + 2y = 27 →
  11. 11.9x + 6y = 81 and 6x + 9y = 99 →
  12. 12.5x + 2y = −15 and 6x + 6y = −36 →
  13. 13.3x + 7y = 38 and 7x + 3y = 22 →
  14. 14.5x + 5y = 60 and 2x − 3y = −21 →
  15. 15.3x + 4y = 5 and 2x − 3y = −8 →
  16. 16.3x + 8y = 87 and 8x + 3y = 67 →
  17. 17.x − y = 7 and 3x + 6y = −15 →
  18. 18.4x + y = 8 and x + 4y = 17 →
  19. 19.x + 4y = 10 and 2x − 5y = 7 →
  20. 20.6x − y = −28 and 6x + 2y = −16 →
  21. 21.x + 7y = 36 and 7x + y = 12 →
  22. 22.2x − 3y = −3 and 6x + 3y = 27 →
  23. 23.5x + 8y = −33 and 8x + 5y = −45 →
  24. 24.5x + y = −18 and 3x − 4y = −20 →
  25. 25.4x − 2y = −20 and 3x + y = 5 →
  26. 26.4x + 3y = −9 and 5x − y = −16 →
  27. 27.4x + 3y = −8 and 3x + 4y = 1 →
  28. 28.3x + 4y = −51 and 4x + 3y = −54 →
  29. 29.3x + 2y = −20 and 4x − 3y = −38 →
  30. 30.4x + 6y = 64 and 2x + 5y = 48 →
  31. 31.6x + 5y = −56 and 5x + 6y = −54 →
  32. 32.3x + 5y = 59 and 5x − y = 33 →
  33. 33.5x − 4y = 44 and 2x − y = 17 →
  34. 34.2x + 6y = 44 and x + 4y = 28 →
  35. 35.2x + 4y = 44 and 4x + 2y = 34 →
  36. 36.6x + 8y = −22 and 8x + 6y = −6 →
  37. 37.4x + 7y = 48 and 7x + 4y = 51 →
  38. 38.5x − 5y = 55 and 2x − y = 20 →
  39. 39.x + 2y = 4 and 4x − 3y = 38 →
  40. 40.x + 5y = −22 and 4x + 3y = −20 →

Answer key

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

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