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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 398 · 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 + y = 6 and 5x − 2y = 44 →
  2. 2.8x + 6y = 60 and 6x + 8y = 66 →
  3. 3.6x + 2y = 56 and 5x − 5y = 20 →
  4. 4.2x + 4y = 20 and x + 3y = 17 →
  5. 5.3x + y = 22 and 5x + y = 40 →
  6. 6.6x + 2y = −2 and 2x + 6y = −38 →
  7. 7.6x + 5y = 54 and 3x + 2y = 24 →
  8. 8.2x + 5y = −24 and 4x + 5y = −8 →
  9. 9.9x + 3y = −42 and 3x + 9y = 42 →
  10. 10.x + 2y = 15 and 6x − y = 51 →
  11. 11.6x + y = 0 and 5x + 6y = 31 →
  12. 12.x − 3y = 22 and 5x + y = −18 →
  13. 13.3x + 5y = 1 and 5x + 4y = −20 →
  14. 14.3x + 7y = 49 and 7x + 3y = 61 →
  15. 15.2x − 4y = −4 and 2x + 5y = 14 →
  16. 16.7x + 2y = 20 and 2x + 7y = −20 →
  17. 17.3x + 2y = 22 and 2x + 3y = 13 →
  18. 18.6x − 6y = −66 and 5x + 4y = 17 →
  19. 19.x + 7y = 14 and 7x + y = 50 →
  20. 20.4x + 6y = 18 and 3x + y = −18 →
  21. 21.2x + 2y = 18 and 6x + y = 44 →
  22. 22.4x + 7y = 65 and 7x + 4y = 56 →
  23. 23.3x + 3y = 6 and 5x + 6y = 13 →
  24. 24.6x − y = 29 and x + 2y = 7 →
  25. 25.2x + y = −2 and x − 5y = −23 →
  26. 26.2x + y = 20 and x + 2y = 19 →
  27. 27.x + 7y = −13 and 7x + y = 5 →
  28. 28.5x − 3y = −9 and x + 3y = 27 →
  29. 29.2x + 2y = −8 and 4x + 6y = −8 →
  30. 30.2x + 3y = 15 and 3x + 2y = 5 →
  31. 31.2x + 2y = −20 and x − 3y = 22 →
  32. 32.8x + 4y = 44 and 4x + 8y = 28 →
  33. 33.3x + 2y = 15 and 4x − 2y = −22 →
  34. 34.4x + 2y = 10 and 6x − 3y = 21 →
  35. 35.3x + y = −8 and 5x + 6y = −9 →
  36. 36.6x − 4y = −84 and 4x − y = −41 →
  37. 37.8x + 9y = 7 and 9x + 8y = 10 →
  38. 38.6x + 6y = −18 and 3x + 5y = −5 →
  39. 39.x + 5y = 28 and 5x + y = 20 →
  40. 40.3x − 5y = −50 and x + 6y = 37 →

Answer key

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

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