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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 704 · 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 + 5y = 8 and 6x + 6y = 18 →
  2. 2.x + 5y = 11 and 4x − y = 23 →
  3. 3.x + 6y = 20 and 2x + 3y = 13 →
  4. 4.6x + y = 10 and 2x + y = 6 →
  5. 5.3x + 2y = 26 and 5x + 2y = 42 →
  6. 6.x + 2y = 5 and 2x + y = 13 →
  7. 7.5x + y = 43 and 3x − 5y = 9 →
  8. 8.4x + y = −13 and 5x + y = −17 →
  9. 9.2x − y = 3 and x − y = 5 →
  10. 10.5x − 2y = −26 and 6x + 3y = 12 →
  11. 11.3x + 3y = 18 and x − 4y = 16 →
  12. 12.5x − 6y = −44 and 6x + 4y = 48 →
  13. 13.4x + 2y = −26 and 4x + 5y = −23 →
  14. 14.6x + 3y = 60 and x + 6y = 54 →
  15. 15.2x − 3y = 6 and x − 2y = 1 →
  16. 16.2x + 9y = 89 and 9x + 2y = 54 →
  17. 17.5x − 6y = −9 and 5x − y = 36 →
  18. 18.3x + 6y = −51 and 6x + y = −14 →
  19. 19.6x + y = 15 and 5x + y = 14 →
  20. 20.2x + 5y = 42 and 5x + 2y = 42 →
  21. 21.6x + 3y = 0 and 2x − 6y = −42 →
  22. 22.6x + 5y = 38 and 5x + 6y = 39 →
  23. 23.2x − 2y = 14 and 4x + 3y = 35 →
  24. 24.5x + 3y = −19 and 4x − 4y = 4 →
  25. 25.2x + 3y = 31 and x + 5y = 47 →
  26. 26.9x + 8y = 79 and 8x + 9y = 74 →
  27. 27.5x − 6y = −9 and 2x + 5y = 26 →
  28. 28.x + 6y = −47 and 6x − 5y = 87 →
  29. 29.4x + 5y = 26 and 5x + 3y = 13 →
  30. 30.7x + 5y = 8 and 5x + 7y = 16 →
  31. 31.7x + 4y = −28 and 4x + 7y = 17 →
  32. 32.6x − 6y = −12 and 4x + 6y = 22 →
  33. 33.3x − 2y = −15 and 4x + 6y = 58 →
  34. 34.8x + 4y = −24 and 4x + 8y = 12 →
  35. 35.4x + 8y = 60 and 8x + 4y = 60 →
  36. 36.x − 6y = 48 and 5x + y = 23 →
  37. 37.x − 5y = 26 and x + 6y = −51 →
  38. 38.x + 5y = 20 and 5x + y = −20 →
  39. 39.3x + 8y = 45 and 8x + 3y = 65 →
  40. 40.6x − 6y = 0 and 4x + 4y = 8 →

Answer key

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

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