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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 997 · 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 + 3y = 24 and 5x + 2y = 49 →
  2. 2.6x − 6y = −90 and 4x + 5y = 21 →
  3. 3.7x + 2y = 10 and 2x + 7y = −55 →
  4. 4.8x + 6y = 72 and 6x + 8y = 68 →
  5. 5.x + 2y = 19 and 2x + y = 20 →
  6. 6.9x + 3y = 69 and 3x + 9y = 15 →
  7. 7.4x + 6y = 2 and 4x + 5y = 7 →
  8. 8.3x + 6y = −15 and 6x − y = 9 →
  9. 9.x + 6y = 37 and 6x + y = 47 →
  10. 10.2x + y = −9 and 6x + 6y = −36 →
  11. 11.3x + 9y = 42 and 9x + 3y = 78 →
  12. 12.7x + 8y = 23 and 8x + 7y = 37 →
  13. 13.3x + 5y = 11 and 4x + y = 26 →
  14. 14.4x + 2y = 30 and 4x + 6y = 34 →
  15. 15.6x + 7y = −26 and 7x + 6y = −13 →
  16. 16.5x + 2y = −30 and 2x − 2y = −26 →
  17. 17.4x + 2y = −8 and 2x + 4y = 8 →
  18. 18.6x + 4y = −8 and 4x + 6y = 18 →
  19. 19.2x + 4y = −22 and 3x − y = 16 →
  20. 20.2x + y = 4 and 2x − 3y = 28 →
  21. 21.2x + 6y = −26 and 3x + y = −15 →
  22. 22.x − 2y = 19 and 5x − 2y = 31 →
  23. 23.x + 5y = 32 and 5x + y = 16 →
  24. 24.4x − y = −13 and 3x + y = −1 →
  25. 25.3x + 6y = 36 and 3x + 4y = 28 →
  26. 26.6x − 6y = −60 and 3x + 2y = 5 →
  27. 27.x + 7y = 43 and 7x + y = −35 →
  28. 28.2x + 4y = 26 and 4x + 2y = 16 →
  29. 29.x − 6y = −6 and 2x + 4y = 20 →
  30. 30.x − 4y = −5 and 6x + 2y = 22 →
  31. 31.5x + 6y = 52 and 5x + 5y = 45 →
  32. 32.6x + 5y = 53 and 2x + 3y = 19 →
  33. 33.6x − 3y = −57 and 3x − 4y = −51 →
  34. 34.3x + 4y = 15 and 4x + 3y = 13 →
  35. 35.5x + y = 51 and x + 5y = 39 →
  36. 36.5x + 2y = 16 and 2x + 5y = 19 →
  37. 37.2x + 2y = 8 and x + 5y = −16 →
  38. 38.5x + 2y = 48 and 2x + 5y = 57 →
  39. 39.5x + 3y = 46 and 2x + 5y = 45 →
  40. 40.4x + 7y = 15 and 7x + 4y = 51 →

Answer key

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

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