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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 978 · 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. 1.2x − 6y = −34 and 2x + 5y = −1 →
  2. 2.3x + 5y = 31 and 5x + 3y = 41 →
  3. 3.4x − 2y = 22 and 2x + 5y = 41 →
  4. 4.6x + 8y = 56 and 8x + 6y = 56 →
  5. 5.x + 3y = 21 and 4x + 5y = 56 →
  6. 6.5x + 3y = −8 and 3x + 5y = 24 →
  7. 7.6x + 6y = 90 and 4x + 6y = 74 →
  8. 8.4x + y = 15 and 6x + 3y = 33 →
  9. 9.6x + 2y = 0 and 5x − 2y = 33 →
  10. 10.2x + 2y = 26 and 5x − 3y = 9 →
  11. 11.6x + 6y = −30 and 2x − 2y = 14 →
  12. 12.3x + 2y = 17 and 5x − 2y = 7 →
  13. 13.x − y = −3 and 2x − y = 2 →
  14. 14.2x + 4y = 44 and 2x + 2y = 30 →
  15. 15.4x + 5y = 13 and 4x + 2y = −14 →
  16. 16.6x − 2y = 10 and 2x + 6y = −50 →
  17. 17.2x + 7y = 60 and 7x + 2y = 30 →
  18. 18.x − 5y = −7 and 6x + 4y = 60 →
  19. 19.8x + 2y = −50 and 2x + 8y = 40 →
  20. 20.4x + 3y = 26 and 2x + 5y = 34 →
  21. 21.7x + y = 49 and x + 7y = −41 →
  22. 22.9x + 6y = 72 and 6x + 9y = 63 →
  23. 23.4x + 2y = 32 and 2x + 4y = 34 →
  24. 24.x − 2y = −14 and 6x + 2y = 42 →
  25. 25.3x + 5y = 40 and 2x + 3y = 25 →
  26. 26.4x + 4y = −28 and 4x + 3y = −26 →
  27. 27.x + 6y = 29 and 6x − 2y = 22 →
  28. 28.5x + 5y = 10 and 2x − 2y = 0 →
  29. 29.3x + 8y = 51 and 8x + 3y = −29 →
  30. 30.6x + 2y = −12 and 2x + 6y = −52 →
  31. 31.x + 4y = −11 and x − 6y = 9 →
  32. 32.2x + 5y = 41 and 5x + 2y = 29 →
  33. 33.4x + 6y = −10 and 6x + 4y = −20 →
  34. 34.4x + 6y = −40 and 2x − 2y = 20 →
  35. 35.4x + 5y = 6 and 5x + 4y = 12 →
  36. 36.6x + y = 38 and x + 4y = 14 →
  37. 37.2x + 5y = 33 and 5x − 4y = 0 →
  38. 38.3x + 4y = −3 and 6x + 4y = 6 →
  39. 39.x − 3y = 17 and x + 4y = −11 →
  40. 40.3x + 6y = 57 and 6x + 3y = 60 →

Answer key

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

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