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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 385 · 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 + 8y = 48 and 8x + 6y = 50 →
  2. 2.6x + 8y = 114 and 8x + 6y = 110 →
  3. 3.5x + 2y = 63 and x + y = 18 →
  4. 4.2x + 2y = 10 and 5x + 4y = 26 →
  5. 5.2x + 3y = 20 and x − 3y = −26 →
  6. 6.x + 7y = −6 and 7x + y = 6 →
  7. 7.6x + y = 43 and x + 4y = 11 →
  8. 8.x + 7y = 36 and 7x + y = −36 →
  9. 9.9x + 5y = 2 and 5x + 9y = 26 →
  10. 10.3x + 7y = −42 and 7x + 3y = −58 →
  11. 11.x + 2y = 1 and 6x − 5y = −62 →
  12. 12.2x + y = 13 and 3x + 5y = 37 →
  13. 13.x + 5y = 26 and 6x + y = −47 →
  14. 14.8x + 6y = 58 and 6x + 8y = 68 →
  15. 15.2x + y = 13 and x + 2y = 17 →
  16. 16.6x + 4y = 32 and x + y = 7 →
  17. 17.4x + 2y = 16 and 2x − 5y = −4 →
  18. 18.5x + 4y = 77 and x + 2y = 25 →
  19. 19.5x + y = 23 and x + 5y = 19 →
  20. 20.x + 3y = 6 and 3x + 4y = 13 →
  21. 21.x + 4y = 17 and 4x + y = −22 →
  22. 22.2x + 6y = 68 and 5x + 4y = 71 →
  23. 23.x + 8y = 77 and 8x + y = 49 →
  24. 24.3x − 2y = 13 and 5x + 6y = 87 →
  25. 25.6x + 5y = −22 and 5x + 6y = −11 →
  26. 26.3x + 2y = 5 and x − 2y = −1 →
  27. 27.9x + y = 5 and x + 9y = −35 →
  28. 28.2x + 6y = 46 and 2x − 2y = −26 →
  29. 29.x + 5y = 13 and 4x − 3y = 29 →
  30. 30.7x + y = 57 and x + 7y = −33 →
  31. 31.4x + 6y = 26 and 6x + 4y = 34 →
  32. 32.2x + 3y = −41 and 3x + 2y = −39 →
  33. 33.x − 5y = −36 and 2x + 3y = 45 →
  34. 34.3x + 2y = 17 and 3x + 3y = 21 →
  35. 35.x + 5y = 6 and 3x + 2y = 5 →
  36. 36.x + y = 7 and 5x + 4y = 33 →
  37. 37.4x − 3y = 1 and 2x − 3y = 11 →
  38. 38.6x − 3y = −48 and 5x − 2y = −36 →
  39. 39.5x + 7y = 79 and 7x + 5y = 77 →
  40. 40.3x + 5y = 59 and x − 3y = −13 →

Answer key

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

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