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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 371 · 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. 1.7x + 2y = 46 and 2x + 7y = 71 →
  2. 2.5x + 3y = −43 and 6x + 6y = −66 →
  3. 3.3x + 8y = 2 and 8x + 3y = 42 →
  4. 4.8x + 5y = −36 and 5x + 8y = −42 →
  5. 5.9x + 7y = −15 and 7x + 9y = −1 →
  6. 6.6x − y = −28 and 4x + 5y = 4 →
  7. 7.3x + 3y = 30 and 5x + 4y = 48 →
  8. 8.3x + y = −1 and 5x − 4y = −47 →
  9. 9.6x − 4y = 32 and 2x + 4y = 16 →
  10. 10.x + 5y = 6 and 5x + y = −42 →
  11. 11.x + 2y = 8 and x + 4y = 20 →
  12. 12.x + 4y = 27 and 6x − 4y = −6 →
  13. 13.3x + 6y = −30 and 2x − 3y = 1 →
  14. 14.x + 4y = 26 and x + 2y = 14 →
  15. 15.2x + 8y = −46 and 8x + 2y = 26 →
  16. 16.3x + 2y = 17 and x + 2y = 7 →
  17. 17.2x − 5y = −27 and 3x + 3y = 54 →
  18. 18.3x + 4y = −26 and 2x − y = 12 →
  19. 19.x − 5y = 1 and 6x + 3y = 39 →
  20. 20.6x + y = 11 and 3x + y = 8 →
  21. 21.6x − y = 36 and 4x + y = 34 →
  22. 22.5x + 2y = 25 and 2x + 5y = 31 →
  23. 23.5x − 6y = 24 and 3x − 4y = 14 →
  24. 24.6x + 2y = −52 and 5x + 5y = −70 →
  25. 25.2x + 6y = 28 and 6x + 2y = 52 →
  26. 26.3x + y = 21 and x − 4y = −6 →
  27. 27.2x + 3y = −2 and 3x + 2y = 2 →
  28. 28.4x + 4y = 16 and 4x + 6y = 22 →
  29. 29.6x − 5y = 59 and 3x − 6y = 54 →
  30. 30.6x − y = −4 and 5x + 4y = −42 →
  31. 31.8x + 3y = 73 and 3x + 8y = 48 →
  32. 32.4x + 5y = 29 and 6x + y = −15 →
  33. 33.4x + 9y = 82 and 9x + 4y = 87 →
  34. 34.x + 5y = −9 and 4x − 2y = 30 →
  35. 35.4x + 9y = −18 and 9x + 4y = −73 →
  36. 36.2x − 4y = −18 and 6x − 3y = 0 →
  37. 37.2x + 9y = 49 and 9x + 2y = 28 →
  38. 38.x + y = −2 and 6x − 4y = 38 →
  39. 39.6x + 2y = 18 and x + 6y = 20 →
  40. 40.2x + 4y = 14 and x + 3y = 8 →

Answer key

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

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