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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 323 · 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 + 6y = 42 and 6x + 2y = 22 →
  2. 2.x + 5y = 26 and 4x + 4y = −8 →
  3. 3.5x − 3y = 50 and x + 3y = −8 →
  4. 4.5x + 6y = −7 and 6x + y = −27 →
  5. 5.5x + y = −12 and 4x − 4y = 24 →
  6. 6.5x − 3y = −43 and 4x + y = −31 →
  7. 7.4x − 2y = −18 and 4x + y = −3 →
  8. 8.5x − 3y = −2 and x + 2y = 23 →
  9. 9.7x + 8y = −18 and 8x + 7y = −27 →
  10. 10.3x + 2y = 20 and 5x + 4y = 36 →
  11. 11.3x − 4y = 8 and 6x + 4y = 64 →
  12. 12.2x + 5y = 3 and 2x + 6y = 4 →
  13. 13.7x + 5y = 3 and 5x + 7y = 9 →
  14. 14.7x + 5y = 9 and 5x + 7y = 3 →
  15. 15.6x + y = 39 and x + 6y = 59 →
  16. 16.2x + 6y = −20 and 6x + 2y = 36 →
  17. 17.2x + 4y = 6 and 5x − 3y = 41 →
  18. 18.4x + 3y = 18 and 3x + 4y = 17 →
  19. 19.9x + 4y = −32 and 4x + 9y = −7 →
  20. 20.5x − 5y = −70 and 2x + y = −1 →
  21. 21.4x + y = 20 and x + 5y = 43 →
  22. 22.2x − 4y = 34 and 3x + 4y = 1 →
  23. 23.6x + 4y = 62 and 4x + y = 28 →
  24. 24.7x + 2y = 13 and 2x + 7y = 23 →
  25. 25.7x + 4y = −11 and 4x + 7y = 22 →
  26. 26.5x + 8y = 61 and 8x + 5y = 43 →
  27. 27.4x − 3y = 49 and 4x − 2y = 42 →
  28. 28.3x + 7y = 55 and 7x + 3y = 35 →
  29. 29.3x + 8y = 38 and 8x + 3y = 28 →
  30. 30.6x + 7y = 45 and 7x + 6y = 33 →
  31. 31.x + 6y = −20 and 6x + y = 20 →
  32. 32.6x + 3y = 42 and 3x + 6y = 30 →
  33. 33.5x − y = −29 and 4x − y = −25 →
  34. 34.3x + 2y = 29 and 4x + 6y = 52 →
  35. 35.2x + 4y = −8 and 2x + 6y = −16 →
  36. 36.4x + 6y = 76 and 3x + 4y = 53 →
  37. 37.6x + 9y = −48 and 9x + 6y = −57 →
  38. 38.5x − 5y = −15 and 2x + 4y = 36 →
  39. 39.5x − 3y = 42 and 3x − 5y = 22 →
  40. 40.4x + y = −17 and 6x + 2y = −24 →

Answer key

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

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