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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 317 · 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. 1.5x + 3y = 21 and 5x + y = 37 →
  2. 2.2x − 3y = 9 and 6x + 4y = 40 →
  3. 3.4x + 7y = −74 and 7x + 4y = −80 →
  4. 4.5x + 4y = 24 and x + 5y = 9 →
  5. 5.x + 2y = 5 and 6x + 5y = 16 →
  6. 6.6x + 2y = 50 and 2x + 6y = 22 →
  7. 7.6x + 2y = 48 and x + 6y = 25 →
  8. 8.4x + 6y = 70 and x − 2y = −14 →
  9. 9.5x − 3y = 21 and 2x − 5y = −3 →
  10. 10.3x − y = −32 and 2x − 6y = −64 →
  11. 11.2x + y = 9 and 5x + 2y = 27 →
  12. 12.2x − y = −18 and 6x + 5y = −22 →
  13. 13.5x + 7y = 14 and 7x + 5y = 34 →
  14. 14.6x − 2y = 22 and 4x − 5y = 11 →
  15. 15.5x + 3y = −47 and 3x + 5y = −57 →
  16. 16.x − y = 4 and 2x − 3y = 16 →
  17. 17.9x + 5y = −5 and 5x + 9y = 47 →
  18. 18.2x + 4y = −10 and x − 4y = 13 →
  19. 19.2x + 4y = 10 and x + y = 4 →
  20. 20.8x + y = 24 and x + 8y = −60 →
  21. 21.3x + 4y = 11 and x + 6y = −1 →
  22. 22.4x − 5y = 2 and 2x − 2y = 0 →
  23. 23.6x + 6y = 90 and 6x + y = 50 →
  24. 24.5x + 2y = 4 and 2x + 5y = −11 →
  25. 25.2x − 2y = 6 and 3x − 2y = 0 →
  26. 26.3x + 6y = 21 and 6x − 4y = −86 →
  27. 27.6x + y = 60 and 4x − 3y = 18 →
  28. 28.6x + 5y = 87 and 3x + 2y = 39 →
  29. 29.6x + 9y = −66 and 9x + 6y = −39 →
  30. 30.2x + 4y = 40 and 5x + 2y = 36 →
  31. 31.4x + 6y = 48 and x + y = 10 →
  32. 32.x + y = 2 and x − y = −8 →
  33. 33.2x + 2y = 10 and x + 5y = 13 →
  34. 34.5x + 7y = 46 and 7x + 5y = 50 →
  35. 35.6x + 4y = −4 and x + 2y = 10 →
  36. 36.3x − 3y = −18 and x − 3y = −24 →
  37. 37.x + 8y = 28 and 8x + y = −28 →
  38. 38.4x − 3y = −20 and 5x − 3y = −19 →
  39. 39.2x − y = −4 and x − 2y = −11 →
  40. 40.6x + 5y = 36 and 3x − 4y = −21 →

Answer key

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

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