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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 434 · 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. 1.4x − 5y = 13 and 3x + 2y = 4 →
  2. 2.8x + 2y = 44 and 2x + 8y = 26 →
  3. 3.4x + y = 4 and x + 4y = −14 →
  4. 4.4x + 8y = 40 and 8x + 4y = 68 →
  5. 5.4x − y = 27 and x + 4y = 28 →
  6. 6.4x + 5y = 43 and 6x − 6y = −30 →
  7. 7.x + y = 14 and x + 3y = 26 →
  8. 8.9x + 2y = −33 and 2x + 9y = −33 →
  9. 9.x + 2y = 13 and 5x + 5y = 40 →
  10. 10.5x + 3y = 30 and 4x + 6y = 42 →
  11. 11.x − y = −14 and x + 6y = 42 →
  12. 12.3x + y = 24 and x + 6y = 25 →
  13. 13.x + 3y = −16 and 6x + 2y = 32 →
  14. 14.x + 6y = 20 and 2x − y = 1 →
  15. 15.3x + 5y = −36 and 5x + 3y = −28 →
  16. 16.6x + 5y = 2 and 5x + 6y = −2 →
  17. 17.x + 6y = 47 and 6x + y = 2 →
  18. 18.2x + 6y = −4 and 6x + 2y = 20 →
  19. 19.6x + 8y = 32 and 8x + 6y = 52 →
  20. 20.7x + 2y = −53 and 2x + 7y = 17 →
  21. 21.x + 6y = 25 and x + 5y = 21 →
  22. 22.5x − 4y = 27 and 6x + y = 44 →
  23. 23.2x − 6y = −46 and x + y = −3 →
  24. 24.9x + 6y = −9 and 6x + 9y = 24 →
  25. 25.6x − 5y = 26 and 5x − 6y = 18 →
  26. 26.6x − 6y = −24 and x + 2y = −7 →
  27. 27.2x + 2y = −2 and x − 4y = 39 →
  28. 28.8x + 3y = 74 and 3x + 8y = 69 →
  29. 29.x + 6y = 57 and 3x + 2y = 27 →
  30. 30.x + 5y = 35 and 2x − 4y = −14 →
  31. 31.5x + 3y = 40 and 3x + 5y = 40 →
  32. 32.4x − 6y = 56 and 4x + 5y = −10 →
  33. 33.x + 3y = 13 and 3x + y = 7 →
  34. 34.2x + 4y = 8 and 5x − 3y = 7 →
  35. 35.2x + y = 1 and x − 5y = −49 →
  36. 36.3x + 3y = 42 and x + 6y = 59 →
  37. 37.3x + 6y = 27 and x − 6y = −15 →
  38. 38.4x + 6y = −20 and 6x + 4y = 10 →
  39. 39.2x + 6y = 38 and x − 6y = −35 →
  40. 40.x + 2y = 5 and 5x + 4y = 13 →

Answer key

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

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