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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 336 · 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 = 4 and 5x + 2y = 14 →
  2. 2.2x + 3y = 7 and x − 2y = 14 →
  3. 3.2x + 4y = −24 and 3x − 4y = −6 →
  4. 4.2x + y = 19 and x + 2y = 14 →
  5. 5.6x − y = 28 and 6x + 5y = 76 →
  6. 6.5x − 6y = −25 and 3x − y = −2 →
  7. 7.x + y = 13 and 6x + y = 33 →
  8. 8.4x + 3y = −7 and 5x − 2y = 20 →
  9. 9.2x + y = 14 and x − 4y = 25 →
  10. 10.4x + 9y = 67 and 9x + 4y = 37 →
  11. 11.5x − 2y = −24 and 2x − y = −8 →
  12. 12.3x + 6y = 33 and x − 6y = −5 →
  13. 13.2x + 6y = 42 and 5x + 3y = 33 →
  14. 14.5x − 5y = 15 and 2x + 4y = −24 →
  15. 15.6x + 2y = −28 and 2x + 6y = −4 →
  16. 16.4x + 6y = 24 and 6x + 4y = 26 →
  17. 17.2x + 4y = 22 and 4x + 2y = 38 →
  18. 18.9x + 8y = 87 and 8x + 9y = 83 →
  19. 19.6x + 2y = 42 and 4x + 2y = 34 →
  20. 20.5x + y = 11 and 4x − 3y = 43 →
  21. 21.4x + 3y = −17 and 3x + 4y = −18 →
  22. 22.x + 4y = 14 and x − y = −1 →
  23. 23.x + 4y = 21 and 3x + 2y = 33 →
  24. 24.2x − 3y = −6 and 5x + 6y = 66 →
  25. 25.6x + 2y = −58 and 2x + 6y = −30 →
  26. 26.5x + 4y = −4 and 4x + 5y = 13 →
  27. 27.3x + 6y = −57 and 3x + 2y = −33 →
  28. 28.6x − 5y = −39 and 6x + 4y = 42 →
  29. 29.8x + 4y = 76 and 4x + 8y = 44 →
  30. 30.8x + 5y = −21 and 5x + 8y = −57 →
  31. 31.3x − 4y = −15 and 2x − y = 5 →
  32. 32.x + 2y = 19 and 2x + y = 23 →
  33. 33.8x + y = 52 and x + 8y = 38 →
  34. 34.2x + 7y = 35 and 7x + 2y = −35 →
  35. 35.x + 3y = 20 and x + 2y = 13 →
  36. 36.x + 4y = 9 and x + 2y = 7 →
  37. 37.x + 4y = 22 and x + 5y = 28 →
  38. 38.3x − 2y = 9 and x − 4y = 13 →
  39. 39.x + 2y = −1 and 2x + y = −8 →
  40. 40.2x + 7y = 19 and 7x + 2y = 44 →

Answer key

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

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