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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 86 · 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. 1.2x + 7y = 77 and 7x + 2y = 67 →
  2. 2.2x + y = 20 and 3x + y = 29 →
  3. 3.4x − 2y = −18 and x − 5y = −36 →
  4. 4.3x + y = −2 and x + 5y = 18 →
  5. 5.x + 6y = 31 and 6x + 2y = 50 →
  6. 6.x − 4y = 28 and 6x + 6y = 18 →
  7. 7.4x + 7y = −53 and 7x + 4y = −68 →
  8. 8.5x + 3y = 35 and 3x + 5y = 37 →
  9. 9.6x + 6y = 18 and 5x − y = 3 →
  10. 10.6x + y = 17 and x + 6y = 32 →
  11. 11.5x + 2y = 13 and 2x + 3y = 14 →
  12. 12.3x + y = 27 and x + 3y = 17 →
  13. 13.4x + 3y = −25 and 3x + 4y = −24 →
  14. 14.6x − 2y = −68 and 5x + y = −38 →
  15. 15.8x + y = −4 and x + 8y = 31 →
  16. 16.2x + 3y = 30 and 4x + 5y = 54 →
  17. 17.7x + 5y = 18 and 5x + 7y = 6 →
  18. 18.4x − 2y = 8 and 5x − y = 1 →
  19. 19.2x + y = −14 and 3x + 5y = −7 →
  20. 20.3x + 6y = −48 and 6x + 2y = −26 →
  21. 21.2x − 5y = −27 and x + 4y = 45 →
  22. 22.x + 9y = 61 and 9x + y = 69 →
  23. 23.x + 4y = −30 and 5x + 2y = −24 →
  24. 24.x + 2y = 17 and 2x + y = 13 →
  25. 25.5x + 3y = −8 and x + y = 2 →
  26. 26.3x + 5y = 37 and 3x − 5y = −13 →
  27. 27.7x + 8y = 91 and 8x + 7y = 89 →
  28. 28.8x + y = 76 and x + 8y = 41 →
  29. 29.8x + 5y = −69 and 5x + 8y = −87 →
  30. 30.6x − 2y = 20 and 4x + 2y = 20 →
  31. 31.x − 4y = 15 and 2x + 2y = 10 →
  32. 32.4x + 2y = 10 and 4x − 5y = −53 →
  33. 33.2x + y = 4 and 4x − y = −16 →
  34. 34.2x + y = 9 and 5x + 6y = 19 →
  35. 35.5x + 5y = 50 and 6x − 4y = 40 →
  36. 36.3x + 5y = 1 and 5x + 3y = 23 →
  37. 37.x − 5y = −36 and 2x + 4y = 54 →
  38. 38.x + 9y = 32 and 9x + y = 48 →
  39. 39.4x + y = 35 and 4x + 6y = 30 →
  40. 40.6x + y = 4 and 5x + 2y = 1 →

Answer key

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

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