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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 817 · 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 − 6y = −24 and 5x − 6y = −23 →
  2. 2.2x + 4y = 22 and 4x + 4y = 36 →
  3. 3.2x + 5y = −13 and 5x + 2y = 20 →
  4. 4.8x + 4y = 84 and 4x + 8y = 96 →
  5. 5.7x + 8y = 97 and 8x + 7y = 98 →
  6. 6.3x + 4y = 2 and 4x + 3y = 5 →
  7. 7.6x + 3y = 12 and 3x + 6y = −3 →
  8. 8.5x + y = 23 and 4x + 3y = 25 →
  9. 9.8x + 2y = 20 and 2x + 8y = 20 →
  10. 10.6x + 4y = 38 and 6x + 3y = 39 →
  11. 11.x + 4y = −11 and 3x − 2y = −5 →
  12. 12.x + 3y = 5 and 2x + 4y = 12 →
  13. 13.2x + 2y = −18 and 3x + 4y = −35 →
  14. 14.7x + 9y = −38 and 9x + 7y = −58 →
  15. 15.3x + 2y = 28 and 2x + 3y = 32 →
  16. 16.x + 4y = 27 and 4x + y = 18 →
  17. 17.3x + 8y = 43 and 8x + 3y = 23 →
  18. 18.5x − 2y = 37 and 4x − 5y = 16 →
  19. 19.x + 4y = 13 and 4x + y = 22 →
  20. 20.2x − 4y = 18 and 2x + 2y = −12 →
  21. 21.6x + 2y = 36 and 2x + 6y = 60 →
  22. 22.2x + 6y = −4 and x + 2y = 1 →
  23. 23.6x + 7y = 69 and 7x + 6y = 61 →
  24. 24.2x + 3y = −17 and 3x + 6y = −36 →
  25. 25.6x − 4y = −50 and 6x + 6y = 30 →
  26. 26.5x + 2y = 21 and x + 3y = 25 →
  27. 27.3x + y = 15 and 3x − 5y = −21 →
  28. 28.3x + 2y = 1 and 3x + 3y = 6 →
  29. 29.x + 5y = 12 and x − 6y = 1 →
  30. 30.6x + 8y = 76 and 8x + 6y = 64 →
  31. 31.x − 5y = 20 and 6x − 6y = 48 →
  32. 32.2x + y = 13 and x + 2y = 11 →
  33. 33.3x + 4y = 29 and 5x − 5y = −10 →
  34. 34.4x + y = 29 and 6x + 5y = 47 →
  35. 35.x + 4y = 19 and 5x + 3y = −7 →
  36. 36.x + 2y = 13 and x − 2y = −3 →
  37. 37.x + 5y = 7 and 5x + y = −13 →
  38. 38.5x + 3y = 18 and 3x + 5y = −2 →
  39. 39.8x + y = 60 and x + 8y = 39 →
  40. 40.6x + 2y = 54 and 2x − 3y = −15 →

Answer key

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

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