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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 174 · 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. 1.8x + 4y = 8 and 4x + 8y = 40 →
  2. 2.x − 4y = −35 and 5x + 5y = 25 →
  3. 3.3x + 3y = 30 and x − 3y = −26 →
  4. 4.6x + 3y = 36 and x − y = 3 →
  5. 5.2x + 5y = 48 and x − 3y = −9 →
  6. 6.3x − y = 14 and 3x + y = 28 →
  7. 7.3x − y = −11 and 4x + 6y = 22 →
  8. 8.6x + 5y = 38 and 6x + y = 46 →
  9. 9.5x − 5y = 20 and 3x + 5y = 44 →
  10. 10.3x + y = 24 and 3x + 3y = 42 →
  11. 11.5x − 5y = −45 and 3x − 4y = −35 →
  12. 12.x + 3y = 28 and 2x + y = 21 →
  13. 13.3x − 3y = −30 and 5x + 5y = −30 →
  14. 14.3x + 3y = 9 and 4x − 3y = −16 →
  15. 15.8x + 7y = −34 and 7x + 8y = −41 →
  16. 16.6x + y = −16 and x − 5y = −13 →
  17. 17.5x + 6y = 39 and 4x − 4y = −4 →
  18. 18.2x + 8y = 42 and 8x + 2y = −12 →
  19. 19.x + 6y = −4 and 6x + 3y = 42 →
  20. 20.x + 6y = 24 and 6x + y = −31 →
  21. 21.3x + y = 22 and x + 3y = 10 →
  22. 22.6x + 6y = 60 and 5x + y = 34 →
  23. 23.4x + 2y = −4 and 6x + y = −10 →
  24. 24.8x + y = 60 and x + 8y = 39 →
  25. 25.2x − 6y = −4 and 3x + 3y = −18 →
  26. 26.x + 6y = −12 and 5x + 5y = −35 →
  27. 27.x + 4y = 45 and 3x + 5y = 72 →
  28. 28.2x + 3y = 3 and 3x + 2y = −3 →
  29. 29.3x + 4y = 18 and 3x + 6y = 24 →
  30. 30.5x − 5y = 10 and 2x + 5y = 32 →
  31. 31.9x + y = −69 and x + 9y = 19 →
  32. 32.6x + 4y = 64 and 4x + 6y = 66 →
  33. 33.2x + 9y = 13 and 9x + 2y = −57 →
  34. 34.x − 5y = −12 and 2x + 4y = 18 →
  35. 35.6x + 6y = 12 and 4x + 5y = 16 →
  36. 36.4x + y = −17 and 2x − 6y = 50 →
  37. 37.3x − y = 17 and x + 4y = 10 →
  38. 38.4x + 3y = 29 and 3x + 4y = 27 →
  39. 39.2x + 4y = 14 and 4x − 4y = 4 →
  40. 40.x + 4y = −23 and x + y = −2 →

Answer key

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

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