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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 227 · 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 + 6y = 32 and 2x + 4y = 16 →
  2. 2.x + 8y = −61 and 8x + y = 16 →
  3. 3.7x + 5y = 60 and 5x + 7y = 60 →
  4. 4.4x + y = −30 and x + 4y = 0 →
  5. 5.3x + 6y = −45 and x + y = −7 →
  6. 6.3x − 5y = 53 and 5x + 3y = 9 →
  7. 7.5x + 9y = −41 and 9x + 5y = 27 →
  8. 8.5x + 4y = −11 and 6x − y = −48 →
  9. 9.2x + 6y = −52 and 5x + 3y = −58 →
  10. 10.5x + 9y = −18 and 9x + 5y = −66 →
  11. 11.5x + 9y = −7 and 9x + 5y = −35 →
  12. 12.2x − y = 14 and 4x − 6y = 12 →
  13. 13.8x + 5y = 112 and 5x + 8y = 109 →
  14. 14.x − 4y = −26 and 4x + 4y = 16 →
  15. 15.4x − 4y = 4 and 4x + 5y = 13 →
  16. 16.5x + 3y = 49 and 3x + 5y = 39 →
  17. 17.9x + 4y = −45 and 4x + 9y = 45 →
  18. 18.2x + 3y = 12 and 3x + 2y = 13 →
  19. 19.7x + 5y = −24 and 5x + 7y = −48 →
  20. 20.x − 3y = −16 and x + 2y = 14 →
  21. 21.6x + 4y = 38 and 4x + 6y = 52 →
  22. 22.4x + 4y = −4 and 4x + y = −28 →
  23. 23.5x + 7y = 14 and 7x + 5y = −14 →
  24. 24.8x + 5y = −55 and 5x + 8y = −49 →
  25. 25.3x − 3y = 27 and 5x − 4y = 38 →
  26. 26.x − 2y = 8 and x − 6y = 16 →
  27. 27.3x + 3y = −21 and 5x − y = −5 →
  28. 28.3x + 6y = 48 and 6x − 3y = −9 →
  29. 29.6x + 4y = 44 and 6x − 5y = 53 →
  30. 30.3x + 4y = 35 and 5x + 5y = 55 →
  31. 31.4x + 7y = 50 and 7x + 4y = 71 →
  32. 32.8x + 9y = 119 and 9x + 8y = 119 →
  33. 33.x − 2y = −16 and x − 5y = −37 →
  34. 34.2x + 6y = 34 and 6x + 2y = 54 →
  35. 35.x + y = 14 and 4x − 5y = 11 →
  36. 36.4x + 3y = 27 and 6x − 3y = 63 →
  37. 37.4x + 9y = 5 and 9x + 4y = −5 →
  38. 38.7x + 3y = −28 and 3x + 7y = −52 →
  39. 39.x + 3y = 13 and 3x + y = 7 →
  40. 40.2x + 5y = 2 and 5x + 2y = −16 →

Answer key

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

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