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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 120 · 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.x − 4y = 34 and 6x − y = 43 →
  2. 2.5x + 4y = 33 and 4x + 5y = 39 →
  3. 3.2x + 6y = 22 and 4x − 5y = 27 →
  4. 4.3x + 5y = 26 and 2x − 2y = 12 →
  5. 5.5x + 5y = 45 and 3x + 5y = 37 →
  6. 6.2x − 3y = −2 and 2x + 4y = 26 →
  7. 7.4x − 2y = 20 and 4x − 6y = 44 →
  8. 8.4x + 8y = 84 and 8x + 4y = 84 →
  9. 9.5x + 6y = −4 and 6x + 5y = −7 →
  10. 10.4x + 3y = 23 and 3x + 4y = 26 →
  11. 11.2x + 7y = −3 and 7x + 2y = 12 →
  12. 12.6x + 8y = 14 and 8x + 6y = −14 →
  13. 13.2x + 5y = 45 and 6x + 6y = 72 →
  14. 14.7x + 3y = 29 and 3x + 7y = 41 →
  15. 15.3x + 3y = 18 and 6x + 3y = 27 →
  16. 16.2x + 6y = 18 and 6x + 2y = −42 →
  17. 17.9x + 4y = 60 and 4x + 9y = 70 →
  18. 18.5x + y = 4 and 5x + 5y = 0 →
  19. 19.6x + y = 3 and 6x + 2y = 12 →
  20. 20.2x + 9y = 14 and 9x + 2y = −14 →
  21. 21.6x + 5y = 22 and x + 4y = −9 →
  22. 22.4x + 2y = 20 and 3x + 6y = 24 →
  23. 23.2x + 2y = −18 and 5x + 3y = −43 →
  24. 24.5x + 2y = 25 and x + 4y = 23 →
  25. 25.5x + 9y = 103 and 9x + 5y = 107 →
  26. 26.6x + 3y = 3 and 2x + 6y = −24 →
  27. 27.3x + 3y = 0 and 2x + 4y = 14 →
  28. 28.3x + 2y = −39 and 2x + 3y = −41 →
  29. 29.6x + 3y = 33 and 3x + 6y = 30 →
  30. 30.3x + 5y = −34 and 3x − y = −4 →
  31. 31.6x + 2y = 28 and 2x + 6y = −28 →
  32. 32.8x + 9y = −90 and 9x + 8y = −97 →
  33. 33.2x + 6y = −54 and 4x − 3y = 12 →
  34. 34.3x + 2y = 3 and 5x − y = 44 →
  35. 35.2x − y = 1 and 5x − y = −8 →
  36. 36.5x − 5y = 50 and x + 3y = 6 →
  37. 37.3x − 2y = 37 and 4x − 4y = 60 →
  38. 38.x + 2y = −9 and 6x − y = −41 →
  39. 39.4x + 4y = 20 and 3x + 4y = 17 →
  40. 40.9x + 8y = 85 and 8x + 9y = 85 →

Answer key

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

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