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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 731 · 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. 1.4x + 2y = −8 and 2x + 2y = 2 →
  2. 2.3x − 6y = 69 and 6x + 6y = −6 →
  3. 3.3x + 4y = 39 and 4x + 3y = 45 →
  4. 4.4x + y = 39 and 2x + 4y = 44 →
  5. 5.8x + 3y = 8 and 3x + 8y = 58 →
  6. 6.x + 6y = 31 and 6x + y = 11 →
  7. 7.2x + 8y = 74 and 8x + 2y = 56 →
  8. 8.6x + 6y = 48 and 6x + 5y = 42 →
  9. 9.9x + 2y = 48 and 2x + 9y = 62 →
  10. 10.2x + 2y = 16 and 6x + 2y = 20 →
  11. 11.x + 6y = 8 and 3x + 6y = 12 →
  12. 12.4x + y = 33 and x + 4y = 27 →
  13. 13.x − 6y = −25 and 3x + 4y = −9 →
  14. 14.x + 3y = 21 and 3x + y = 23 →
  15. 15.7x + 5y = 38 and 5x + 7y = 10 →
  16. 16.5x − 5y = −75 and 3x − 2y = −38 →
  17. 17.7x + 3y = 69 and 3x + 7y = 81 →
  18. 18.5x − 2y = 16 and x + y = 6 →
  19. 19.6x + 2y = 64 and 2x + 6y = 64 →
  20. 20.5x + 4y = 50 and x + 2y = 16 →
  21. 21.x + 3y = 26 and 3x + y = 22 →
  22. 22.6x + 9y = 105 and 9x + 6y = 90 →
  23. 23.6x − 3y = −24 and x + 4y = −13 →
  24. 24.2x + y = 12 and 5x + 4y = 33 →
  25. 25.4x + 6y = 38 and x + 3y = 14 →
  26. 26.2x + 2y = 22 and 4x − 5y = −10 →
  27. 27.x + 3y = 35 and 3x + y = 33 →
  28. 28.4x − y = 26 and 5x + y = 19 →
  29. 29.5x − y = 5 and 3x + 2y = 16 →
  30. 30.2x − 5y = 21 and 4x + 6y = 26 →
  31. 31.6x − 6y = −36 and x + 6y = 43 →
  32. 32.3x + 2y = 25 and 2x + 3y = 20 →
  33. 33.6x + y = −44 and 4x − 5y = −18 →
  34. 34.7x + 6y = 30 and 6x + 7y = 22 →
  35. 35.2x + 7y = 60 and 7x + 2y = 30 →
  36. 36.5x − 2y = −24 and 6x + 3y = 9 →
  37. 37.9x + 6y = 0 and 6x + 9y = 15 →
  38. 38.2x + y = 25 and 3x + 3y = 48 →
  39. 39.6x + 3y = 39 and x + 5y = 38 →
  40. 40.3x + 3y = −21 and 5x + y = −15 →

Answer key

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

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