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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 203 · 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. 1.4x − 5y = 26 and 3x + 3y = 33 →
  2. 2.2x + y = 8 and x + 2y = 13 →
  3. 3.4x + 2y = 40 and 5x − y = 43 →
  4. 4.6x + 6y = 84 and 4x + 3y = 50 →
  5. 5.x + 5y = 14 and 4x + 4y = 40 →
  6. 6.2x + 4y = −4 and 2x + 3y = −7 →
  7. 7.5x + 3y = 23 and 3x + y = 9 →
  8. 8.6x + 5y = 73 and 2x + 4y = 36 →
  9. 9.x + 7y = 36 and 7x + y = 60 →
  10. 10.3x − 6y = 12 and x + y = 10 →
  11. 11.2x + 2y = 28 and 2x − y = 4 →
  12. 12.2x − 6y = −38 and 5x − 4y = −51 →
  13. 13.6x + 6y = 60 and 5x + 4y = 42 →
  14. 14.9x + y = 21 and x + 9y = 29 →
  15. 15.5x + 8y = 49 and 8x + 5y = 55 →
  16. 16.x + 5y = 18 and 4x − 6y = −6 →
  17. 17.5x + 7y = 58 and 7x + 5y = 38 →
  18. 18.5x − y = 39 and 2x − y = 21 →
  19. 19.2x + 2y = 0 and 3x − 5y = −16 →
  20. 20.4x − 4y = −28 and 6x − 2y = −22 →
  21. 21.9x + 6y = −6 and 6x + 9y = −24 →
  22. 22.6x − y = 13 and 4x + 4y = −24 →
  23. 23.4x + 2y = 44 and 5x + y = 49 →
  24. 24.x + y = −16 and 5x + y = −48 →
  25. 25.5x + 4y = 37 and 5x + 2y = 31 →
  26. 26.2x + 2y = 6 and 2x − 4y = −18 →
  27. 27.x + 8y = −55 and 8x + y = 1 →
  28. 28.9x + 8y = 79 and 8x + 9y = 74 →
  29. 29.3x + 9y = 3 and 9x + 3y = 57 →
  30. 30.x + y = −1 and 2x − 6y = 14 →
  31. 31.9x + y = 19 and x + 9y = −69 →
  32. 32.6x + y = −41 and 4x + 3y = −25 →
  33. 33.2x + y = 4 and 6x − 6y = 84 →
  34. 34.5x + 5y = −50 and 6x + 5y = −59 →
  35. 35.6x + 7y = 37 and 7x + 6y = 41 →
  36. 36.5x + 4y = 41 and 3x + 5y = 35 →
  37. 37.6x + 2y = 36 and x + 6y = −28 →
  38. 38.8x + 7y = −18 and 7x + 8y = −12 →
  39. 39.6x + 3y = −30 and x + 6y = 28 →
  40. 40.4x − 6y = −66 and 2x + 5y = 39 →

Answer key

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

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