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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 825 · 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 + 4y = 15 and x − 4y = −11 →
  2. 2.x + 5y = 10 and 2x − 6y = 4 →
  3. 3.3x + 4y = −25 and 3x + 3y = −21 →
  4. 4.5x − 2y = −36 and x − 5y = −21 →
  5. 5.3x + 4y = 15 and 4x + 3y = 13 →
  6. 6.5x + y = 31 and 2x + 6y = 46 →
  7. 7.5x − 2y = 42 and x − 3y = 24 →
  8. 8.2x + y = 6 and x + 2y = 6 →
  9. 9.4x − 2y = −18 and 2x − 3y = −15 →
  10. 10.2x + 6y = 48 and x − 5y = −16 →
  11. 11.3x + 5y = 11 and 4x + 6y = 16 →
  12. 12.x + 5y = −20 and 6x + y = 25 →
  13. 13.5x − 3y = 26 and 2x − 6y = −4 →
  14. 14.x + 6y = 50 and x − y = −13 →
  15. 15.4x + 9y = 27 and 9x + 4y = 77 →
  16. 16.3x + 5y = 29 and 2x + 5y = 26 →
  17. 17.x + 2y = −25 and 4x − 2y = −20 →
  18. 18.2x − 3y = 10 and 3x + 2y = −37 →
  19. 19.4x + 6y = 6 and 6x − 5y = 51 →
  20. 20.8x + 5y = −5 and 5x + 8y = −47 →
  21. 21.3x + y = −20 and 5x + 4y = −24 →
  22. 22.x + 2y = 13 and 2x + y = 20 →
  23. 23.x − 3y = −14 and x + 6y = 13 →
  24. 24.6x + y = 14 and 4x − 2y = 4 →
  25. 25.6x + 2y = 22 and 6x + y = 26 →
  26. 26.x − 4y = −15 and 5x + y = −33 →
  27. 27.2x − 3y = −40 and 4x + y = −24 →
  28. 28.4x − 3y = −4 and 4x + 4y = 52 →
  29. 29.5x − 6y = 16 and 6x − 4y = 32 →
  30. 30.5x + 6y = 76 and 5x − 2y = 28 →
  31. 31.5x − 6y = −19 and 4x + 3y = 55 →
  32. 32.x − 4y = 31 and 6x + 4y = −10 →
  33. 33.6x − 3y = 48 and 2x + y = 20 →
  34. 34.4x + 2y = 20 and 5x + 2y = 24 →
  35. 35.5x + 7y = 47 and 7x + 5y = 61 →
  36. 36.x + 6y = 35 and 3x − 4y = −49 →
  37. 37.3x + y = 22 and 3x + 4y = 25 →
  38. 38.3x − y = 11 and 3x + 5y = −37 →
  39. 39.7x + 8y = 41 and 8x + 7y = 49 →
  40. 40.x + 5y = 27 and 6x + 5y = 62 →

Answer key

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

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