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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 374 · 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 − 3y = 11 and 6x − 6y = 36 →
  2. 2.6x + 9y = 21 and 9x + 6y = 39 →
  3. 3.8x + y = −17 and x + 8y = 53 →
  4. 4.3x + 7y = 44 and 7x + 3y = 36 →
  5. 5.3x + 5y = 43 and 5x + 3y = 45 →
  6. 6.2x − 5y = 11 and 3x − 2y = 0 →
  7. 7.3x − 4y = 19 and x + 4y = 1 →
  8. 8.3x + 5y = 41 and x − y = −5 →
  9. 9.9x + 5y = 54 and 5x + 9y = 86 →
  10. 10.5x + 3y = 9 and 3x + 3y = −3 →
  11. 11.4x − y = 12 and 6x + y = −2 →
  12. 12.5x − 6y = −47 and x + 5y = 3 →
  13. 13.2x + 6y = 12 and 6x + 2y = 52 →
  14. 14.5x + y = 43 and 3x − 2y = 31 →
  15. 15.2x + y = 5 and x + 5y = 16 →
  16. 16.5x − 3y = −17 and 2x + 4y = 40 →
  17. 17.6x − 4y = −16 and 6x + 3y = −9 →
  18. 18.2x − 4y = −8 and 3x + 3y = −3 →
  19. 19.8x + 9y = −2 and 9x + 8y = 2 →
  20. 20.4x + 6y = 42 and 3x + 5y = 32 →
  21. 21.3x + 6y = 9 and 6x + 3y = 45 →
  22. 22.2x + 6y = −34 and 5x + 5y = −45 →
  23. 23.x + 2y = 17 and 4x + 2y = 26 →
  24. 24.3x + y = −14 and x + 5y = 28 →
  25. 25.3x − 5y = 19 and 4x − 5y = 27 →
  26. 26.2x + 4y = 28 and 6x − y = 45 →
  27. 27.2x − y = 11 and 3x − 2y = 19 →
  28. 28.6x + 3y = −18 and 6x − y = −2 →
  29. 29.7x + 3y = −4 and 3x + 7y = 44 →
  30. 30.9x + 8y = 12 and 8x + 9y = 22 →
  31. 31.x + 6y = −51 and 6x + y = −26 →
  32. 32.x + 3y = 14 and 3x − y = 2 →
  33. 33.5x + 6y = 47 and 4x − 3y = −17 →
  34. 34.5x + y = 11 and x + y = 7 →
  35. 35.2x + 5y = 46 and 5x + 2y = 31 →
  36. 36.6x + 5y = 51 and 5x + 6y = 48 →
  37. 37.9x + 2y = −52 and 2x + 9y = −80 →
  38. 38.4x + 9y = −105 and 9x + 4y = −90 →
  39. 39.5x + 5y = 45 and 6x + 3y = 48 →
  40. 40.x − 4y = 21 and x + 3y = 0 →

Answer key

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

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