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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 857 · 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. 1.3x + 6y = 39 and 6x + 3y = 24 →
  2. 2.3x + 5y = 46 and 5x + 3y = 50 →
  3. 3.2x + y = −7 and x + 2y = 7 →
  4. 4.8x + 2y = 24 and 2x + 8y = −54 →
  5. 5.x + 5y = −33 and 2x − 3y = 38 →
  6. 6.6x + 4y = 42 and x − 2y = −17 →
  7. 7.5x + 2y = 14 and 6x + y = 14 →
  8. 8.x + 2y = −1 and 2x + y = 10 →
  9. 9.2x + 6y = 38 and 2x + 2y = 22 →
  10. 10.x + 7y = 22 and 7x + y = 10 →
  11. 11.5x + 4y = 4 and 3x − 5y = −42 →
  12. 12.2x − 2y = 22 and 5x − 2y = 46 →
  13. 13.4x + 4y = −12 and x − 2y = −6 →
  14. 14.4x − 5y = 7 and x − 5y = −2 →
  15. 15.4x + 6y = 0 and 6x + 6y = 6 →
  16. 16.6x + 3y = 3 and 3x + 6y = −21 →
  17. 17.2x − 4y = 0 and x + 2y = −16 →
  18. 18.2x − 5y = 3 and 4x + 5y = 21 →
  19. 19.4x + 2y = −28 and x − 3y = 21 →
  20. 20.6x − 3y = 15 and x + 5y = 8 →
  21. 21.6x + 7y = 25 and 7x + 6y = 27 →
  22. 22.3x − 6y = −30 and 5x + 4y = 48 →
  23. 23.x − 2y = 12 and 5x − 2y = 36 →
  24. 24.5x + 2y = 9 and 2x + 5y = 33 →
  25. 25.2x + 5y = 32 and 6x + y = 12 →
  26. 26.5x + 7y = −74 and 7x + 5y = −70 →
  27. 27.6x + 7y = 12 and 7x + 6y = 1 →
  28. 28.4x + 2y = 26 and 2x + 4y = 16 →
  29. 29.5x + 9y = −62 and 9x + 5y = −22 →
  30. 30.5x + 5y = 20 and x − 2y = 7 →
  31. 31.x + 4y = 30 and 4x + y = −15 →
  32. 32.5x − 5y = −35 and 5x + y = 19 →
  33. 33.5x + 2y = 24 and 5x − 6y = 48 →
  34. 34.6x + 2y = 46 and 5x + 2y = 40 →
  35. 35.4x + 3y = 46 and 3x + 4y = 45 →
  36. 36.2x + 2y = −4 and x + 3y = −20 →
  37. 37.x − y = −1 and 5x + 5y = −25 →
  38. 38.7x + 4y = 23 and 4x + 7y = 32 →
  39. 39.2x + y = 3 and 5x − 5y = 45 →
  40. 40.5x − 2y = 3 and 6x + 2y = 8 →

Answer key

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

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