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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 93 · 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 + y = −21 and 6x + 2y = −18 →
  2. 2.7x + y = 2 and x + 7y = −34 →
  3. 3.8x + 3y = 30 and 3x + 8y = 25 →
  4. 4.7x + 5y = 61 and 5x + 7y = 71 →
  5. 5.2x + 5y = −15 and 6x − 4y = 50 →
  6. 6.6x − 5y = −26 and 6x − y = −10 →
  7. 7.x + 3y = 0 and 3x + y = 8 →
  8. 8.x + 6y = 62 and 3x + 6y = 78 →
  9. 9.4x − 6y = 56 and 6x + 4y = 32 →
  10. 10.6x + 3y = 36 and 2x − y = 0 →
  11. 11.2x + 5y = 31 and 5x + 2y = 25 →
  12. 12.6x + 2y = 30 and x + 2y = −10 →
  13. 13.x + 6y = 48 and 6x + y = 43 →
  14. 14.4x + 4y = 12 and 3x − 3y = 21 →
  15. 15.6x + 9y = −57 and 9x + 6y = −78 →
  16. 16.6x − 2y = −22 and 3x + 2y = −5 →
  17. 17.x + y = 3 and x + 5y = 27 →
  18. 18.x + 3y = −1 and 2x − 3y = −11 →
  19. 19.4x + 6y = 30 and 2x + 4y = 18 →
  20. 20.5x − 5y = −5 and 2x − 3y = 5 →
  21. 21.6x + 5y = 69 and 6x + 2y = 42 →
  22. 22.6x + 9y = 36 and 9x + 6y = 39 →
  23. 23.x − 3y = −13 and 4x + 6y = 20 →
  24. 24.8x + 2y = 50 and 2x + 8y = 80 →
  25. 25.3x + 4y = 44 and 5x + 5y = 60 →
  26. 26.8x + y = 25 and x + 8y = 74 →
  27. 27.5x − 3y = 19 and 4x + 3y = −1 →
  28. 28.7x + 8y = 85 and 8x + 7y = 80 →
  29. 29.3x + 6y = 48 and 6x + 4y = 48 →
  30. 30.5x + 5y = 40 and 4x + 2y = 28 →
  31. 31.5x + 4y = −25 and x + 6y = −31 →
  32. 32.6x − 4y = −20 and 2x + 3y = 2 →
  33. 33.9x + 4y = −49 and 4x + 9y = −29 →
  34. 34.6x + 5y = −74 and 4x + 4y = −52 →
  35. 35.3x − 2y = 8 and 2x + 2y = 32 →
  36. 36.x + 6y = 11 and 6x + y = 31 →
  37. 37.x + 4y = 23 and 3x − 2y = 13 →
  38. 38.3x − 3y = 3 and 4x + y = 14 →
  39. 39.2x − 3y = −19 and 5x + 6y = 47 →
  40. 40.4x − 5y = 44 and 6x + 3y = 24 →

Answer key

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

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