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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 186 · 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 = 48 and x − 2y = −7 →
  2. 2.4x + 8y = 0 and 8x + 4y = 12 →
  3. 3.x + 3y = −16 and 3x + y = 8 →
  4. 4.4x − 3y = 5 and x − 5y = 31 →
  5. 5.5x + y = 5 and x + 5y = −23 →
  6. 6.3x − 4y = 6 and x − 5y = 24 →
  7. 7.6x + 5y = 89 and 5x + 6y = 87 →
  8. 8.3x + 6y = 45 and x + 4y = 21 →
  9. 9.x + 6y = 51 and 2x − 2y = −10 →
  10. 10.3x + 3y = −6 and 5x − 3y = −66 →
  11. 11.x + 4y = 11 and 4x + y = 14 →
  12. 12.x + y = 1 and x + 5y = 25 →
  13. 13.5x + 2y = 49 and 2x + 5y = 28 →
  14. 14.2x − 4y = −42 and 2x + 4y = 22 →
  15. 15.2x + 3y = 6 and 6x + 3y = 30 →
  16. 16.5x − y = −29 and 5x + y = −41 →
  17. 17.x + 2y = 15 and 2x + y = 12 →
  18. 18.x + 5y = −3 and 4x − 3y = 34 →
  19. 19.x + 3y = −25 and x − 4y = 24 →
  20. 20.5x − 5y = −40 and 5x + 6y = 26 →
  21. 21.4x + 4y = −24 and x − 6y = −20 →
  22. 22.3x + 3y = −6 and 6x − 6y = 48 →
  23. 23.3x + 6y = −9 and 4x + 2y = −24 →
  24. 24.7x + 5y = −28 and 5x + 7y = −44 →
  25. 25.5x + 2y = 43 and 6x − 4y = −6 →
  26. 26.2x + 6y = 46 and 5x + 6y = 52 →
  27. 27.x + 6y = 11 and 6x + y = −4 →
  28. 28.3x + 7y = 51 and 7x + 3y = 39 →
  29. 29.2x − y = 12 and 6x − 2y = 28 →
  30. 30.3x − 6y = 21 and 2x − y = 5 →
  31. 31.3x + 6y = 30 and 6x + 3y = −3 →
  32. 32.x + 6y = −3 and 3x + y = 25 →
  33. 33.x + 6y = 48 and 6x + y = 43 →
  34. 34.5x + 3y = 13 and 5x − 3y = 7 →
  35. 35.x + 6y = −11 and 2x + 3y = −13 →
  36. 36.x + 9y = −71 and 9x + y = 1 →
  37. 37.3x + 3y = −6 and x + 3y = −8 →
  38. 38.6x + y = −28 and 2x − 6y = −22 →
  39. 39.x − 5y = 33 and 5x + y = 35 →
  40. 40.7x + 5y = 38 and 5x + 7y = 34 →

Answer key

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

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