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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 629 · 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. 1.8x + y = −12 and x + 8y = 30 →
  2. 2.4x + 3y = 40 and 3x + 4y = 44 →
  3. 3.5x + 8y = 11 and 8x + 5y = 41 →
  4. 4.6x + 2y = 8 and 2x + 6y = −24 →
  5. 5.x − 5y = 39 and 5x − 5y = 55 →
  6. 6.6x + 5y = −44 and 5x − 5y = −55 →
  7. 7.2x + 4y = 52 and 4x + 2y = 50 →
  8. 8.2x + 4y = 2 and x − 3y = 6 →
  9. 9.3x + 6y = 33 and 6x + 2y = −4 →
  10. 10.5x + 3y = −28 and 3x + 5y = −4 →
  11. 11.7x + 3y = 51 and 3x + 7y = 39 →
  12. 12.4x + y = 13 and x + 4y = 22 →
  13. 13.2x + 9y = 97 and 9x + 2y = 90 →
  14. 14.6x + 5y = −4 and 3x + 6y = −30 →
  15. 15.2x − 3y = 2 and x + 2y = 15 →
  16. 16.9x + 7y = 66 and 7x + 9y = 62 →
  17. 17.6x + 2y = 62 and 5x − 5y = 25 →
  18. 18.2x + 4y = 22 and 4x + 5y = 20 →
  19. 19.x − 3y = 2 and 3x + 6y = 21 →
  20. 20.2x + y = 13 and 4x − 3y = 21 →
  21. 21.x + 4y = 1 and 4x − 5y = −17 →
  22. 22.6x + y = 48 and 5x − 6y = −1 →
  23. 23.5x − 5y = −20 and 6x − 4y = −26 →
  24. 24.6x + 5y = 3 and 6x − 6y = −30 →
  25. 25.4x + 9y = −11 and 9x + 4y = −41 →
  26. 26.5x − 6y = −22 and x + 5y = 39 →
  27. 27.6x + 6y = 0 and 4x − 2y = 24 →
  28. 28.x + 3y = −12 and 5x + y = −32 →
  29. 29.6x + 5y = −49 and 3x − 4y = 8 →
  30. 30.x − 4y = −16 and 2x + 4y = 4 →
  31. 31.6x + 4y = −38 and 4x + 6y = −12 →
  32. 32.x + 6y = 15 and 5x + 3y = 48 →
  33. 33.x + 6y = −52 and 2x − 3y = 31 →
  34. 34.5x − y = 8 and x − 6y = −39 →
  35. 35.4x + 8y = 52 and 8x + 4y = −4 →
  36. 36.5x − 5y = −15 and 3x + 3y = −27 →
  37. 37.6x + 3y = 9 and 3x + 6y = 27 →
  38. 38.2x + 3y = 14 and 3x + 2y = 1 →
  39. 39.6x − 4y = −2 and x − 6y = −11 →
  40. 40.5x + y = 41 and 2x + 3y = 32 →

Answer key

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

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