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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 663 · 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 + 2y = 4 and 2x + 6y = −4 →
  2. 2.2x + 9y = −99 and 9x + 2y = −99 →
  3. 3.x − 2y = −7 and 3x − 3y = −15 →
  4. 4.5x + 5y = −5 and 6x − 6y = −90 →
  5. 5.4x + 3y = −17 and 2x + 6y = −22 →
  6. 6.3x + 6y = −9 and x − y = −6 →
  7. 7.5x + 4y = 42 and 4x + 5y = 39 →
  8. 8.2x + 8y = −6 and 8x + 2y = 36 →
  9. 9.x + 3y = −26 and 5x + 3y = −34 →
  10. 10.5x + 5y = 5 and 5x − 4y = 50 →
  11. 11.6x + 6y = 36 and 3x − 6y = −9 →
  12. 12.2x + 3y = 36 and 3x + 2y = 34 →
  13. 13.5x + 5y = −15 and x + 5y = 1 →
  14. 14.2x + y = 4 and 6x + 4y = 18 →
  15. 15.5x + 3y = −22 and 6x − 6y = −36 →
  16. 16.5x + 2y = 8 and 6x + 2y = 10 →
  17. 17.7x + 3y = 55 and 3x + 7y = 35 →
  18. 18.3x + 5y = 42 and 5x + 3y = 22 →
  19. 19.x + 4y = 41 and 4x + y = 29 →
  20. 20.4x + 6y = −2 and 6x + 4y = −8 →
  21. 21.5x − 6y = −11 and x + 2y = 17 →
  22. 22.4x + 9y = 100 and 9x + 4y = 95 →
  23. 23.6x + y = −60 and x + 6y = −45 →
  24. 24.7x + 8y = 73 and 8x + 7y = 77 →
  25. 25.2x + 3y = 9 and 3x + 2y = 11 →
  26. 26.6x − y = 40 and 2x + y = 16 →
  27. 27.5x + 6y = −16 and 4x − 3y = −44 →
  28. 28.2x + 3y = 26 and 3x + 2y = 19 →
  29. 29.x + 5y = −12 and 4x − 4y = 24 →
  30. 30.6x + 4y = 18 and 4x + 6y = 22 →
  31. 31.x + 4y = 27 and 3x + 6y = 45 →
  32. 32.3x + 3y = 33 and 6x + 5y = 60 →
  33. 33.3x + 3y = 24 and x + 3y = 14 →
  34. 34.x + 9y = 1 and 9x + y = −71 →
  35. 35.x − 3y = 11 and 4x − 3y = −10 →
  36. 36.6x + 5y = 7 and 5x + 6y = 4 →
  37. 37.x + y = 13 and 4x − 4y = 20 →
  38. 38.5x + 5y = −35 and x + 4y = −19 →
  39. 39.3x + 2y = 13 and 5x + 3y = 23 →
  40. 40.x + 5y = 38 and 6x − 4y = −78 →

Answer key

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

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