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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 854 · 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. 1.6x − 2y = 42 and x − y = 5 →
  2. 2.6x − y = −16 and 6x − 5y = −8 →
  3. 3.3x + 4y = 29 and 5x − y = −13 →
  4. 4.2x + 2y = −2 and 3x − y = 5 →
  5. 5.5x + 6y = −26 and 6x + 2y = 0 →
  6. 6.5x + 2y = 34 and 5x − 3y = −1 →
  7. 7.2x + y = 13 and 5x + 3y = 37 →
  8. 8.2x + 3y = −21 and 3x + 2y = −29 →
  9. 9.3x − y = −5 and x + y = 9 →
  10. 10.x + 5y = 10 and 5x + y = −22 →
  11. 11.5x − 5y = 10 and 6x + 2y = 28 →
  12. 12.2x + 6y = −50 and 6x + 2y = −6 →
  13. 13.5x − 6y = 9 and 4x + 3y = −24 →
  14. 14.4x − 4y = 44 and x − 5y = 19 →
  15. 15.x − 6y = −14 and 4x − 6y = −38 →
  16. 16.3x + 6y = 27 and 2x + y = 15 →
  17. 17.5x + 2y = 44 and 2x + 6y = 54 →
  18. 18.3x + y = 21 and x + 3y = 15 →
  19. 19.3x + 6y = −24 and 6x + 3y = −21 →
  20. 20.3x − 5y = 9 and 6x + 2y = −54 →
  21. 21.3x + 2y = 11 and 2x + 3y = 4 →
  22. 22.6x + 9y = 30 and 9x + 6y = −15 →
  23. 23.3x − 4y = −3 and 5x + y = −28 →
  24. 24.6x + 8y = 62 and 8x + 6y = 78 →
  25. 25.4x + 6y = 84 and 3x + 3y = 51 →
  26. 26.2x − 2y = −4 and 5x + 4y = 17 →
  27. 27.3x − 4y = −9 and 3x − 2y = −3 →
  28. 28.x − 6y = −47 and 3x + 3y = 27 →
  29. 29.2x + 5y = 23 and 5x + 2y = 26 →
  30. 30.x + y = 11 and 6x + 5y = 58 →
  31. 31.6x + 2y = 54 and 2x + 6y = 66 →
  32. 32.2x + 4y = −12 and 4x + 3y = −29 →
  33. 33.x − y = 5 and 3x − 4y = 12 →
  34. 34.5x + y = 25 and 4x − 2y = 6 →
  35. 35.2x + 3y = 24 and 6x + 2y = 44 →
  36. 36.x + 3y = 10 and 4x + 4y = 8 →
  37. 37.5x + 4y = 46 and 5x + 6y = 64 →
  38. 38.4x − 3y = −8 and 2x + 6y = −34 →
  39. 39.5x − 4y = 6 and 6x + 4y = −28 →
  40. 40.x + 7y = −15 and 7x + y = −9 →

Answer key

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

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