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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 47 · 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 = −53 and 5x + 2y = 8 →
  2. 2.8x + 5y = 99 and 5x + 8y = 96 →
  3. 3.6x + 4y = 28 and x + 2y = 2 →
  4. 4.5x + 4y = −37 and 2x + 6y = −28 →
  5. 5.2x + 2y = −24 and 5x + y = −24 →
  6. 6.x + 5y = 46 and 6x + y = 15 →
  7. 7.x − 3y = −15 and x + 6y = 39 →
  8. 8.x − y = 6 and 2x − y = 13 →
  9. 9.6x + 5y = 64 and 4x + 2y = 40 →
  10. 10.6x − 3y = 18 and 4x + 4y = 60 →
  11. 11.5x + 4y = 76 and 4x + 5y = 77 →
  12. 12.6x − y = 42 and 2x − 5y = −14 →
  13. 13.5x + 3y = 33 and 6x + 2y = 30 →
  14. 14.4x + 2y = −34 and 2x + 4y = −44 →
  15. 15.3x + 3y = 24 and 4x + 5y = 38 →
  16. 16.4x + y = 11 and 5x + 6y = 9 →
  17. 17.3x − 3y = 54 and x − 2y = 27 →
  18. 18.x + 4y = 38 and 3x + y = 15 →
  19. 19.6x − 2y = −44 and 2x − 2y = −24 →
  20. 20.4x + y = 9 and 3x + y = 7 →
  21. 21.4x + 6y = −34 and 2x + 4y = −24 →
  22. 22.6x + 3y = 45 and x + 6y = 13 →
  23. 23.3x − 3y = −45 and x − 2y = −23 →
  24. 24.7x + 6y = 63 and 6x + 7y = 67 →
  25. 25.4x + 9y = 17 and 9x + 4y = 22 →
  26. 26.4x + 5y = 46 and x + y = 11 →
  27. 27.2x − 3y = −34 and 2x − y = −18 →
  28. 28.8x + 4y = −96 and 4x + 8y = −96 →
  29. 29.3x + 5y = 40 and 5x + 3y = 40 →
  30. 30.3x + 5y = 19 and 5x + 3y = 21 →
  31. 31.9x + 5y = −82 and 5x + 9y = −58 →
  32. 32.2x − 5y = −31 and 2x + 6y = 46 →
  33. 33.3x − 5y = −28 and 3x + 5y = 22 →
  34. 34.x + 8y = 79 and 8x + y = 65 →
  35. 35.4x + 3y = −36 and 3x + 4y = −41 →
  36. 36.x + 4y = −10 and 4x − y = −23 →
  37. 37.5x + 2y = 43 and 2x + 2y = 16 →
  38. 38.2x + 3y = −10 and 5x + y = −12 →
  39. 39.x − 6y = 25 and 2x + 2y = −6 →
  40. 40.5x + 2y = 27 and 2x + 5y = 36 →

Answer key

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

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