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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 112 · 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 + 6y = 24 and 2x + 5y = 23 →
  2. 2.4x + 3y = 4 and 3x + 4y = 10 →
  3. 3.7x + 3y = 75 and 3x + 7y = 55 →
  4. 4.x − 4y = 32 and 6x + 5y = −69 →
  5. 5.7x + 5y = 48 and 5x + 7y = 48 →
  6. 6.x + 3y = 3 and x + 2y = 1 →
  7. 7.3x + 4y = −15 and 2x + y = −15 →
  8. 8.3x + 6y = 24 and 3x + 3y = 9 →
  9. 9.2x + 3y = 10 and 6x + 4y = −10 →
  10. 10.6x + 7y = −62 and 7x + 6y = −68 →
  11. 11.4x + 5y = −47 and 3x + 4y = −37 →
  12. 12.2x + 3y = 24 and 2x − 3y = 0 →
  13. 13.2x + 4y = 12 and 4x + 2y = 12 →
  14. 14.5x + 4y = 23 and 2x + y = 5 →
  15. 15.3x + 5y = −47 and x − 2y = 10 →
  16. 16.5x + y = −16 and x + 5y = −8 →
  17. 17.3x + 5y = 8 and 5x + 2y = 26 →
  18. 18.7x + 6y = 83 and 6x + 7y = 86 →
  19. 19.4x − 5y = −68 and x + 5y = 33 →
  20. 20.5x + 5y = −40 and 3x + 6y = −51 →
  21. 21.x − 3y = 14 and 5x + 4y = −6 →
  22. 22.5x + 2y = 12 and 3x + 3y = 9 →
  23. 23.2x + 7y = 54 and 7x + 2y = 9 →
  24. 24.5x + 5y = 10 and x + 5y = −14 →
  25. 25.4x + 2y = 24 and 2x + 4y = 24 →
  26. 26.2x + 4y = 0 and 4x + 2y = 12 →
  27. 27.5x + 4y = −24 and 4x + 5y = −21 →
  28. 28.5x − y = 12 and 4x + 3y = 2 →
  29. 29.2x + y = 15 and 4x + y = 25 →
  30. 30.7x + 4y = −33 and 4x + 7y = 0 →
  31. 31.x + 2y = 19 and 4x − 4y = −8 →
  32. 32.2x + 2y = 4 and 2x + 4y = −6 →
  33. 33.4x + 5y = 57 and 5x + 4y = 60 →
  34. 34.2x + 5y = 49 and 6x + 6y = 66 →
  35. 35.6x − y = 44 and 2x − y = 12 →
  36. 36.x + y = 3 and 6x − y = 25 →
  37. 37.5x + 4y = 2 and 4x + 5y = 7 →
  38. 38.3x + 3y = 39 and 2x + 3y = 34 →
  39. 39.3x + 4y = 9 and 4x + 3y = 19 →
  40. 40.6x − 6y = 18 and x + 6y = 45 →

Answer key

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

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