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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 745 · 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. 1.8x + 7y = 82 and 7x + 8y = 83 →
  2. 2.x − 5y = 19 and 2x + y = −6 →
  3. 3.6x − y = 47 and x + 2y = −3 →
  4. 4.4x − 6y = 48 and 4x + 4y = 28 →
  5. 5.6x + 5y = 7 and 5x + 6y = −7 →
  6. 6.3x − y = 10 and 5x + 6y = 78 →
  7. 7.4x + 5y = −13 and 5x + 4y = −23 →
  8. 8.2x + 8y = −22 and 8x + 2y = −28 →
  9. 9.7x + 9y = 66 and 9x + 7y = 62 →
  10. 10.4x + 6y = 40 and 5x + 2y = 39 →
  11. 11.6x − 6y = −36 and 2x + y = 9 →
  12. 12.2x + 7y = −17 and 7x + 2y = −37 →
  13. 13.3x + 8y = 75 and 8x + 3y = 90 →
  14. 14.4x − 6y = −22 and x − 2y = −9 →
  15. 15.x + 2y = 5 and 5x + 6y = 5 →
  16. 16.3x + 3y = 15 and 2x + y = 6 →
  17. 17.5x + 4y = −35 and 6x + 6y = −48 →
  18. 18.x + 9y = −24 and 9x + y = 24 →
  19. 19.x + 4y = 24 and 6x + 5y = −8 →
  20. 20.5x + 6y = −48 and 6x + 5y = −51 →
  21. 21.x + 8y = 37 and 8x + y = 44 →
  22. 22.5x + 3y = 37 and 4x + y = 24 →
  23. 23.2x − y = −20 and 3x − 5y = −44 →
  24. 24.5x + 2y = 9 and 4x − y = 2 →
  25. 25.3x + 6y = 27 and 3x − 5y = −17 →
  26. 26.4x + 4y = 60 and 6x + 3y = 66 →
  27. 27.3x + 2y = 0 and 2x + 3y = 5 →
  28. 28.2x + 5y = 14 and 6x − 4y = 4 →
  29. 29.5x + 3y = −16 and 4x + 5y = −31 →
  30. 30.x + 6y = 14 and 5x + 5y = 45 →
  31. 31.3x + 7y = 31 and 7x + 3y = 19 →
  32. 32.2x + 7y = −14 and 7x + 2y = 41 →
  33. 33.7x + 6y = 27 and 6x + 7y = 25 →
  34. 34.2x + 2y = 16 and 4x + 2y = 20 →
  35. 35.3x − 5y = −55 and 6x − 2y = −46 →
  36. 36.3x + 2y = 6 and 4x + 5y = 22 →
  37. 37.x + y = 1 and 3x − 4y = 17 →
  38. 38.2x + y = 13 and x + 2y = 11 →
  39. 39.4x + 4y = 8 and 2x − 5y = −3 →
  40. 40.3x − 3y = −27 and x − 2y = −16 →

Answer key

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

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