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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 932 · 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 + 3y = 19 and 6x + 3y = 54 →
  2. 2.3x + 3y = −36 and x + 5y = −28 →
  3. 3.4x − 5y = 10 and 6x + y = 32 →
  4. 4.8x + 4y = 36 and 4x + 8y = 48 →
  5. 5.5x + 5y = 30 and 5x + 3y = 12 →
  6. 6.4x + y = −8 and x + y = 4 →
  7. 7.2x − 2y = 18 and 6x + y = 47 →
  8. 8.3x − 4y = −20 and 4x + 6y = −4 →
  9. 9.2x + 2y = 14 and 6x + 5y = 37 →
  10. 10.7x + y = 27 and x + 7y = 45 →
  11. 11.3x + 5y = 31 and x + 5y = 37 →
  12. 12.x + 2y = −9 and 2x + y = −9 →
  13. 13.x − 6y = 3 and 2x + 4y = −26 →
  14. 14.x + 5y = 35 and 4x + 4y = 44 →
  15. 15.3x + y = 18 and 6x − 5y = 57 →
  16. 16.2x − 3y = 40 and x + 5y = −32 →
  17. 17.5x + 3y = 53 and 3x + 5y = 51 →
  18. 18.4x + 2y = −30 and 5x + 3y = −42 →
  19. 19.4x + 3y = 37 and 6x + 3y = 45 →
  20. 20.4x − y = −9 and 5x + y = −9 →
  21. 21.2x − 6y = 22 and 6x + y = 47 →
  22. 22.4x + 6y = 50 and 3x + 4y = 34 →
  23. 23.6x − y = 2 and 5x − 4y = −11 →
  24. 24.4x − y = −14 and 6x + 3y = −12 →
  25. 25.7x + 9y = −98 and 9x + 7y = −94 →
  26. 26.3x + 8y = 32 and 8x + 3y = 67 →
  27. 27.x − 5y = 47 and x − y = 11 →
  28. 28.2x + 5y = 61 and 6x − 2y = 30 →
  29. 29.5x + y = −22 and 4x + 6y = −54 →
  30. 30.4x + 5y = 43 and 2x + 2y = 20 →
  31. 31.x − y = −11 and x + 5y = 43 →
  32. 32.7x + y = 4 and x + 7y = −20 →
  33. 33.2x + y = 7 and x + 2y = 17 →
  34. 34.9x + 6y = −24 and 6x + 9y = 24 →
  35. 35.x + 5y = 14 and 4x − 6y = 4 →
  36. 36.9x + 4y = −34 and 4x + 9y = 21 →
  37. 37.3x − 4y = 9 and 5x + 5y = 50 →
  38. 38.5x + 2y = −22 and 6x + 5y = −29 →
  39. 39.3x + 6y = −12 and x + 3y = −8 →
  40. 40.5x + 4y = −31 and x − 6y = −13 →

Answer key

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

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