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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 182 · 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 − 5y = 8 and 4x − 4y = 4 →
  2. 2.7x + y = 58 and x + 7y = 70 →
  3. 3.3x − y = 16 and 5x + 5y = 80 →
  4. 4.5x + 7y = 48 and 7x + 5y = 24 →
  5. 5.x + 3y = −24 and 3x + y = 0 →
  6. 6.3x + 6y = 33 and x − 6y = 3 →
  7. 7.2x + 6y = 72 and x + 4y = 45 →
  8. 8.5x − 4y = 21 and 5x + 6y = 81 →
  9. 9.2x + 6y = 12 and 4x + y = −31 →
  10. 10.5x + 6y = 60 and 3x + 4y = 38 →
  11. 11.3x + 4y = 34 and 5x − 4y = −18 →
  12. 12.2x + 6y = −26 and 3x + 4y = −4 →
  13. 13.2x + 3y = 16 and 3x + 2y = 19 →
  14. 14.2x + 4y = 8 and 6x − 4y = −40 →
  15. 15.x + 4y = 1 and 4x + y = −11 →
  16. 16.2x + 2y = 26 and x + 2y = 22 →
  17. 17.4x + 2y = 18 and 2x + 2y = 10 →
  18. 18.3x − 2y = −2 and 5x + 6y = −22 →
  19. 19.4x + 4y = 24 and 5x − 4y = 12 →
  20. 20.4x + y = 43 and x + 4y = 37 →
  21. 21.6x − 5y = 27 and x − 4y = 14 →
  22. 22.x + 6y = 41 and x − y = −15 →
  23. 23.x + 8y = 47 and 8x + y = 61 →
  24. 24.9x + y = 49 and x + 9y = 41 →
  25. 25.x + 7y = 64 and 7x + y = 16 →
  26. 26.x − 2y = −13 and 6x − 3y = −15 →
  27. 27.7x + y = −55 and x + 7y = 47 →
  28. 28.2x + 7y = 36 and 7x + 2y = 36 →
  29. 29.x + 7y = −7 and 7x + y = 47 →
  30. 30.6x − 3y = 15 and x + 5y = −3 →
  31. 31.8x + 3y = −96 and 3x + 8y = −91 →
  32. 32.2x + 5y = −41 and x − 4y = 12 →
  33. 33.5x − 6y = 10 and x − y = 3 →
  34. 34.2x + 5y = −24 and 6x + 4y = −50 →
  35. 35.2x + y = −6 and x + 2y = 3 →
  36. 36.3x + 6y = 60 and 2x + y = 16 →
  37. 37.2x + 2y = 4 and 2x + 4y = −4 →
  38. 38.5x − 4y = 6 and 5x + 3y = 13 →
  39. 39.6x + y = 30 and x + 6y = 40 →
  40. 40.2x + 9y = −14 and 9x + 2y = 14 →

Answer key

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

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