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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 421 · 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. 1.7x + y = 49 and x + 7y = 55 →
  2. 2.3x + 4y = 3 and 4x + 3y = 18 →
  3. 3.9x + 6y = 45 and 6x + 9y = 15 →
  4. 4.x + 6y = 57 and 6x + y = 27 →
  5. 5.9x + 7y = 60 and 7x + 9y = 68 →
  6. 6.x + y = 2 and 4x + 6y = 22 →
  7. 7.5x + 2y = −25 and 2x + 5y = 11 →
  8. 8.3x + y = 34 and x + 3y = 30 →
  9. 9.3x + 7y = 31 and 7x + 3y = 19 →
  10. 10.6x + 2y = −16 and 2x + 6y = 16 →
  11. 11.x + 5y = 32 and 5x + y = 40 →
  12. 12.6x + y = −14 and x + 6y = 21 →
  13. 13.4x + 2y = 40 and x + y = 14 →
  14. 14.6x + 6y = 48 and 2x − 4y = 4 →
  15. 15.5x + 2y = 2 and 3x − y = 10 →
  16. 16.x + 8y = 35 and 8x + y = 28 →
  17. 17.x + 3y = 33 and x − 3y = −15 →
  18. 18.4x + 2y = 2 and 2x + 4y = −26 →
  19. 19.8x + y = 2 and x + 8y = −47 →
  20. 20.5x − 4y = −1 and 5x + 3y = −8 →
  21. 21.2x + 4y = 54 and 6x + 5y = 99 →
  22. 22.6x − y = 37 and 4x − 4y = 8 →
  23. 23.x − y = 17 and x + 2y = −7 →
  24. 24.5x + y = 11 and 3x + 6y = 12 →
  25. 25.5x + 3y = 52 and x + 4y = 41 →
  26. 26.6x + y = −23 and x + 3y = 16 →
  27. 27.8x + 9y = 6 and 9x + 8y = 11 →
  28. 28.8x + 3y = 42 and 3x + 8y = 57 →
  29. 29.6x − 4y = −14 and 3x + 5y = −56 →
  30. 30.4x + 3y = 15 and 3x + 4y = −1 →
  31. 31.7x + 2y = 29 and 2x + 7y = −11 →
  32. 32.5x − 2y = 31 and 2x + 6y = −42 →
  33. 33.3x − 4y = −17 and 3x + 2y = 13 →
  34. 34.6x + 2y = 36 and 5x + 2y = 29 →
  35. 35.6x + 2y = 10 and 2x + 6y = 46 →
  36. 36.6x + 2y = 20 and 5x + 3y = 26 →
  37. 37.5x + 3y = 52 and 2x + 5y = 55 →
  38. 38.3x + 8y = −53 and 8x + 3y = −68 →
  39. 39.6x + 9y = −105 and 9x + 6y = −90 →
  40. 40.x − 4y = −29 and 2x + y = 23 →

Answer key

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

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