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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 946 · 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. 1.9x + 3y = 30 and 3x + 9y = 66 →
  2. 2.5x + 3y = −4 and 2x + y = −2 →
  3. 3.6x − 6y = 12 and 2x + 6y = −28 →
  4. 4.4x + 5y = 36 and 2x + y = 6 →
  5. 5.6x + 2y = −24 and 2x + 6y = −24 →
  6. 6.9x + 2y = −12 and 2x + 9y = 23 →
  7. 7.9x + 5y = 48 and 5x + 9y = 8 →
  8. 8.6x + y = 9 and 3x + 5y = 18 →
  9. 9.5x − 6y = 34 and 6x − 2y = 46 →
  10. 10.7x + 5y = 19 and 5x + 7y = 17 →
  11. 11.5x − 2y = 51 and 6x + 5y = 39 →
  12. 12.9x + 8y = 11 and 8x + 9y = 23 →
  13. 13.5x + 3y = 48 and x + y = 12 →
  14. 14.x + 9y = 26 and 9x + y = 74 →
  15. 15.x + 4y = −15 and 3x + 6y = −33 →
  16. 16.x + 4y = −5 and 4x + 2y = −34 →
  17. 17.4x + 4y = −28 and 2x + 6y = −6 →
  18. 18.6x − 3y = −3 and 5x + 4y = 43 →
  19. 19.4x + 6y = −78 and 5x − 3y = −3 →
  20. 20.2x + 7y = 25 and 7x + 2y = −25 →
  21. 21.3x + 2y = 13 and 3x + 4y = 23 →
  22. 22.3x + y = 25 and 5x + 5y = 55 →
  23. 23.3x + 6y = 12 and 5x + y = −34 →
  24. 24.6x + 5y = −29 and x − y = 8 →
  25. 25.2x + y = −16 and x − 2y = −3 →
  26. 26.5x + y = 16 and 6x + y = 21 →
  27. 27.6x − 2y = 6 and 6x − 6y = −18 →
  28. 28.5x + 3y = −33 and 5x + 6y = −51 →
  29. 29.3x + 4y = −20 and 4x + 4y = −16 →
  30. 30.8x + 5y = −23 and 5x + 8y = 10 →
  31. 31.x + 9y = −79 and 9x + y = 9 →
  32. 32.9x + 2y = 76 and 2x + 9y = 34 →
  33. 33.6x + 4y = 84 and 4x + 6y = 86 →
  34. 34.x + 5y = 26 and 5x + y = 34 →
  35. 35.5x + y = −3 and x + 5y = 9 →
  36. 36.x + 6y = 60 and x + 3y = 33 →
  37. 37.6x + 3y = 3 and 4x − 3y = 27 →
  38. 38.2x + 5y = 41 and 3x + 3y = 30 →
  39. 39.6x − 5y = 3 and 5x − 6y = −3 →
  40. 40.4x − 3y = −14 and 4x + 2y = 16 →

Answer key

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

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