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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 808 · 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. 1.9x + 3y = 39 and 3x + 9y = 69 →
  2. 2.3x + 5y = 67 and 5x + 3y = 69 →
  3. 3.3x + 4y = 22 and x + y = 6 →
  4. 4.5x + 2y = 13 and 6x − 2y = −2 →
  5. 5.2x + 2y = −8 and 2x + 5y = −2 →
  6. 6.4x + y = −20 and x + 4y = 25 →
  7. 7.3x + 2y = 26 and 2x − 4y = −20 →
  8. 8.3x + 6y = −24 and 2x + 5y = −24 →
  9. 9.8x + 7y = 52 and 7x + 8y = 53 →
  10. 10.5x + 2y = −39 and x − 2y = 9 →
  11. 11.4x + y = 24 and x + 3y = 28 →
  12. 12.6x − 6y = −6 and 2x − 5y = −26 →
  13. 13.5x − 5y = −5 and 3x + 4y = 25 →
  14. 14.5x + 3y = 1 and 3x + 5y = −9 →
  15. 15.4x + 7y = 30 and 7x + 4y = 3 →
  16. 16.4x + 9y = 53 and 9x + 4y = 38 →
  17. 17.3x + 2y = 27 and 6x + 6y = 60 →
  18. 18.4x + 3y = −15 and 3x + 4y = −13 →
  19. 19.6x + 3y = −6 and 3x − 6y = 57 →
  20. 20.5x − 2y = 17 and 2x + 3y = 22 →
  21. 21.2x + 7y = −9 and 7x + 2y = −54 →
  22. 22.4x − 6y = −8 and 4x + 5y = 14 →
  23. 23.6x + y = 61 and x + 6y = 51 →
  24. 24.9x + 6y = 30 and 6x + 9y = 30 →
  25. 25.8x + 7y = 22 and 7x + 8y = 23 →
  26. 26.7x + y = −36 and x + 7y = −12 →
  27. 27.5x + 3y = 11 and 3x + 5y = −19 →
  28. 28.6x + 7y = −71 and 7x + 6y = −72 →
  29. 29.2x + 4y = 44 and 5x − y = 11 →
  30. 30.4x + 3y = −25 and 5x + 6y = −47 →
  31. 31.5x − 5y = −15 and 5x + y = 33 →
  32. 32.8x + 2y = −74 and 2x + 8y = −26 →
  33. 33.x + 4y = 36 and x + y = 12 →
  34. 34.5x + y = 8 and x + 5y = −8 →
  35. 35.3x + 6y = −57 and 4x − 4y = −16 →
  36. 36.2x + 6y = −38 and 6x + 4y = −2 →
  37. 37.6x + y = 12 and 6x − 2y = −6 →
  38. 38.2x + 5y = 34 and 6x + 2y = 24 →
  39. 39.2x + y = −8 and x + 2y = 8 →
  40. 40.6x + y = 42 and x + 6y = 42 →

Answer key

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

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