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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 767 · 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 + 3y = −12 and x + 3y = 2 →
  2. 2.2x + 4y = 20 and x − 5y = −18 →
  3. 3.9x + 8y = −95 and 8x + 9y = −92 →
  4. 4.2x + 4y = 10 and 3x + 2y = 11 →
  5. 5.5x + 2y = 19 and 5x + 4y = 23 →
  6. 6.5x + 2y = 1 and x + 2y = −3 →
  7. 7.2x + 2y = 18 and 4x + 2y = 28 →
  8. 8.6x + 4y = 30 and 4x + 6y = 0 →
  9. 9.4x + y = 10 and x − 3y = 9 →
  10. 10.6x − 3y = −57 and 6x + 5y = −1 →
  11. 11.4x + 2y = −14 and 2x + 4y = 20 →
  12. 12.6x + y = −47 and 5x + y = −39 →
  13. 13.3x − 3y = −27 and 2x − y = −12 →
  14. 14.4x − 6y = 60 and x + 4y = −18 →
  15. 15.8x + 4y = 0 and 4x + 8y = 12 →
  16. 16.2x + 5y = −11 and 5x + 5y = −5 →
  17. 17.5x + y = 8 and x + 5y = −8 →
  18. 18.6x + 3y = 18 and 3x + 6y = 27 →
  19. 19.x + y = 9 and 4x + 6y = 38 →
  20. 20.7x + 4y = −29 and 4x + 7y = −59 →
  21. 21.2x + 4y = 48 and 4x + 2y = 42 →
  22. 22.3x + 6y = 45 and 6x + 3y = 27 →
  23. 23.9x + y = −70 and x + 9y = 10 →
  24. 24.2x − 2y = −8 and 5x + 6y = 57 →
  25. 25.x + 4y = −13 and 4x + 6y = −12 →
  26. 26.3x − 2y = −41 and 2x − 3y = −39 →
  27. 27.6x + 6y = 12 and 2x − 2y = −24 →
  28. 28.x − y = −4 and 2x − y = 0 →
  29. 29.4x + 9y = 55 and 9x + 4y = 10 →
  30. 30.6x + 3y = −18 and x − 2y = −8 →
  31. 31.3x + 7y = 67 and 7x + 3y = 63 →
  32. 32.x − 4y = −29 and 4x + y = 20 →
  33. 33.7x + y = −49 and x + 7y = 41 →
  34. 34.6x + 8y = −6 and 8x + 6y = 6 →
  35. 35.4x + 9y = −14 and 9x + 4y = −64 →
  36. 36.6x + 5y = 2 and 5x − 4y = 18 →
  37. 37.5x + y = −14 and 2x + 5y = −1 →
  38. 38.3x − 4y = 39 and 5x + 2y = 13 →
  39. 39.5x + 6y = 38 and 3x − y = 9 →
  40. 40.7x + 2y = 81 and 2x + 7y = 81 →

Answer key

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

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