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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 361 · 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 = −67 and 6x + y = −41 →
  2. 2.5x + 5y = 15 and x − 6y = −4 →
  3. 3.5x − 5y = −75 and x + 5y = 39 →
  4. 4.4x + 4y = 60 and 2x + 3y = 37 →
  5. 5.x + 3y = −2 and 3x + y = 10 →
  6. 6.6x + 3y = 21 and 3x + 6y = 33 →
  7. 7.x + 9y = −25 and 9x + y = 15 →
  8. 8.5x + 4y = −49 and 5x + 3y = −48 →
  9. 9.2x + 5y = −23 and 2x − 6y = 54 →
  10. 10.7x + 9y = 13 and 9x + 7y = 35 →
  11. 11.x + 5y = −1 and 4x − 2y = 18 →
  12. 12.8x + 4y = 84 and 4x + 8y = 72 →
  13. 13.x + y = 6 and 5x − 6y = −3 →
  14. 14.6x + 4y = 0 and 4x + 2y = −6 →
  15. 15.x − 3y = −30 and x − 6y = −57 →
  16. 16.2x + 5y = 1 and 5x + 2y = 13 →
  17. 17.2x + y = 8 and x − y = 7 →
  18. 18.6x − 6y = −30 and 3x + 2y = −5 →
  19. 19.3x + 2y = 18 and 2x + 5y = 23 →
  20. 20.5x − 2y = 15 and 4x + y = 25 →
  21. 21.x + 2y = −20 and 2x + y = −22 →
  22. 22.7x + 5y = 52 and 5x + 7y = 68 →
  23. 23.5x + 5y = 10 and 4x + 5y = 9 →
  24. 24.5x − 2y = −21 and 3x − y = −11 →
  25. 25.4x − y = 10 and 2x + 2y = 10 →
  26. 26.9x + 3y = −66 and 3x + 9y = −78 →
  27. 27.5x + y = 25 and 2x − 5y = −17 →
  28. 28.x + 9y = 62 and 9x + y = 78 →
  29. 29.4x + y = 29 and x + 4y = 41 →
  30. 30.6x − 4y = −34 and 2x + 2y = −8 →
  31. 31.8x + 3y = −99 and 3x + 8y = −99 →
  32. 32.3x + 3y = 9 and x + 4y = −9 →
  33. 33.2x + 3y = −16 and 6x + 5y = −32 →
  34. 34.6x + 6y = −36 and 2x − y = −3 →
  35. 35.3x + 2y = 29 and 3x + y = 25 →
  36. 36.5x + 3y = 69 and 3x + 5y = 67 →
  37. 37.4x + 4y = 16 and x + 5y = 28 →
  38. 38.4x − y = −34 and 6x + 2y = −58 →
  39. 39.5x + 2y = −33 and x + 2y = −5 →
  40. 40.6x − 5y = −13 and 5x + y = 15 →

Answer key

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

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