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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 886 · 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. 1.3x + 7y = −6 and 7x + 3y = −54 →
  2. 2.2x − 5y = 37 and 2x + 5y = −13 →
  3. 3.x − y = 11 and 5x + 6y = 33 →
  4. 4.x − 5y = −29 and 2x + 3y = −6 →
  5. 5.2x + 6y = 50 and 5x − 3y = −19 →
  6. 6.6x + 6y = −30 and 3x + 6y = −21 →
  7. 7.4x − y = 8 and 4x + 3y = 24 →
  8. 8.3x + 8y = 28 and 8x + 3y = 38 →
  9. 9.x + 3y = 22 and 3x + y = −6 →
  10. 10.5x + 6y = 66 and 4x + 2y = 36 →
  11. 11.5x + 3y = 18 and 2x + 3y = 9 →
  12. 12.6x + y = 23 and 2x + 2y = 6 →
  13. 13.3x − 3y = 15 and 2x + 4y = 16 →
  14. 14.2x + y = −5 and x + 6y = 25 →
  15. 15.5x + 6y = −41 and 4x + 5y = −34 →
  16. 16.5x + 3y = 21 and 4x + 4y = 20 →
  17. 17.6x + y = 52 and x + 6y = −3 →
  18. 18.4x + y = 22 and 5x + 5y = 50 →
  19. 19.4x − 5y = 11 and 4x − 4y = 8 →
  20. 20.x + 6y = −26 and 6x + y = −16 →
  21. 21.4x + 5y = 43 and 3x − 6y = 3 →
  22. 22.7x + 2y = 5 and 2x + 7y = −5 →
  23. 23.x − 4y = 27 and 5x + 6y = −21 →
  24. 24.5x + 4y = 18 and 4x − 4y = 0 →
  25. 25.2x + y = 14 and 2x + 5y = −2 →
  26. 26.3x − 2y = 9 and 5x − y = 36 →
  27. 27.2x − 2y = −20 and 3x − 2y = −29 →
  28. 28.9x + 6y = 81 and 6x + 9y = 69 →
  29. 29.x + 4y = 39 and 3x − y = 13 →
  30. 30.5x + 4y = 44 and 6x + 5y = 54 →
  31. 31.2x + 5y = −26 and 5x + 2y = −23 →
  32. 32.5x − 4y = −35 and 4x − y = −17 →
  33. 33.4x − 6y = −26 and 6x + y = 31 →
  34. 34.6x + 8y = 34 and 8x + 6y = 8 →
  35. 35.8x + 9y = 81 and 9x + 8y = 89 →
  36. 36.6x − 5y = −3 and 6x + 2y = 18 →
  37. 37.4x + 7y = −67 and 7x + 4y = −76 →
  38. 38.3x − 6y = 15 and 4x + 6y = −22 →
  39. 39.6x + 6y = −24 and 6x − 3y = 30 →
  40. 40.3x − 3y = 18 and 6x + 2y = 52 →

Answer key

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

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