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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 355 · 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 + 6y = 72 and 6x + 4y = 54 →
  2. 2.4x + 4y = 28 and 6x + 4y = 40 →
  3. 3.2x + 5y = 20 and 5x + 2y = 29 →
  4. 4.8x + 9y = −18 and 9x + 8y = −33 →
  5. 5.x + 6y = 10 and 3x + 2y = −18 →
  6. 6.x + 2y = 12 and 2x + y = 0 →
  7. 7.4x + 3y = 16 and 3x + 4y = 26 →
  8. 8.x + 2y = 15 and 6x + 2y = 40 →
  9. 9.4x + 5y = 10 and 3x + 3y = 9 →
  10. 10.9x + 8y = 37 and 8x + 9y = 31 →
  11. 11.6x + 7y = 48 and 7x + 6y = 43 →
  12. 12.x + y = −3 and 6x − 2y = −10 →
  13. 13.5x + 3y = 21 and x + 6y = −12 →
  14. 14.3x + 4y = −25 and 5x + 6y = −41 →
  15. 15.3x − 4y = −16 and 2x + 6y = 50 →
  16. 16.4x + 6y = −34 and 6x + 4y = −46 →
  17. 17.2x − y = −16 and x + 6y = 5 →
  18. 18.6x − 6y = 36 and 4x − 5y = 33 →
  19. 19.3x + 5y = 23 and 5x + 3y = 17 →
  20. 20.3x + 2y = 17 and 2x + 3y = 13 →
  21. 21.6x + 5y = 99 and 5x + 6y = 99 →
  22. 22.x − 2y = −3 and 6x − 4y = 14 →
  23. 23.3x + 2y = 17 and 5x + 6y = 31 →
  24. 24.6x + 2y = −22 and 2x + 6y = −2 →
  25. 25.6x + 6y = 54 and x − 5y = −3 →
  26. 26.x − 6y = −10 and 2x + 6y = 16 →
  27. 27.3x − 2y = −32 and x + 5y = 12 →
  28. 28.6x + y = 40 and 2x − 4y = 22 →
  29. 29.x + y = −4 and x + 6y = 1 →
  30. 30.7x + 4y = 52 and 4x + 7y = 25 →
  31. 31.x + 3y = −3 and 3x + y = −25 →
  32. 32.6x + 8y = −64 and 8x + 6y = −76 →
  33. 33.2x + 6y = 40 and 2x − y = −16 →
  34. 34.3x + 6y = −57 and 4x + y = −41 →
  35. 35.4x + 5y = −1 and 5x + y = −17 →
  36. 36.x + 8y = 23 and 8x + y = −5 →
  37. 37.5x + y = 29 and x + 5y = −23 →
  38. 38.7x + 9y = 26 and 9x + 7y = 6 →
  39. 39.6x + 2y = 46 and 6x − 2y = 14 →
  40. 40.2x + 9y = 29 and 9x + 2y = 15 →

Answer key

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

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