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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 41 · 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. 1.2x + 2y = −12 and 6x + 3y = −12 →
  2. 2.9x + 3y = 27 and 3x + 9y = −39 →
  3. 3.3x − 4y = −16 and 5x + 4y = 48 →
  4. 4.2x + 4y = 6 and 4x + 2y = 6 →
  5. 5.x + 7y = 13 and 7x + y = 43 →
  6. 6.2x + 6y = −38 and 5x − 3y = 49 →
  7. 7.4x − y = 37 and 5x + 3y = 25 →
  8. 8.2x + 5y = 49 and 5x + 2y = 49 →
  9. 9.2x − 5y = −38 and x + 6y = 32 →
  10. 10.3x − y = 3 and 5x + 2y = 16 →
  11. 11.5x + 8y = −16 and 8x + 5y = −49 →
  12. 12.2x + 4y = −24 and 5x + 5y = −25 →
  13. 13.x + 5y = 12 and 5x + y = 12 →
  14. 14.2x + 3y = 34 and 2x + y = 18 →
  15. 15.4x + 6y = 60 and 4x + 2y = 44 →
  16. 16.3x + 6y = −6 and 5x − 4y = 18 →
  17. 17.4x + y = −5 and x + 4y = −35 →
  18. 18.2x + y = 16 and x + 2y = 17 →
  19. 19.5x + 8y = 25 and 8x + 5y = 1 →
  20. 20.3x − y = −3 and 4x − y = −2 →
  21. 21.x − 5y = −15 and 5x + 2y = 33 →
  22. 22.2x + 8y = −50 and 8x + 2y = −80 →
  23. 23.3x − 2y = −1 and x − 5y = 17 →
  24. 24.x − 2y = 10 and 2x + 2y = −22 →
  25. 25.4x + 6y = −12 and x + 3y = −9 →
  26. 26.3x + 4y = 47 and 4x + 3y = 44 →
  27. 27.3x + 3y = −6 and x − 6y = 54 →
  28. 28.x + 3y = 10 and 2x − 2y = 4 →
  29. 29.2x − 4y = −10 and 6x − 2y = 20 →
  30. 30.3x + 6y = 57 and 2x − 2y = −4 →
  31. 31.2x − 3y = 16 and 2x + 5y = −32 →
  32. 32.5x + 3y = −4 and 3x + 5y = 4 →
  33. 33.3x + 8y = 77 and 8x + 3y = 77 →
  34. 34.6x + 4y = 44 and 5x + 3y = 35 →
  35. 35.9x + 3y = −24 and 3x + 9y = −24 →
  36. 36.7x + 8y = 36 and 8x + 7y = 39 →
  37. 37.2x + 4y = 14 and 6x + 5y = 7 →
  38. 38.9x + y = 28 and x + 9y = 12 →
  39. 39.6x + 9y = −72 and 9x + 6y = −93 →
  40. 40.3x − 3y = 6 and 4x + 2y = 44 →

Answer key

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

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