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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 287 · 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 + 4y = 22 and 4x + 2y = 38 →
  2. 2.3x + y = −1 and 4x + 6y = −34 →
  3. 3.5x + 5y = 15 and x − 5y = −39 →
  4. 4.6x + 2y = 20 and x + 2y = 0 →
  5. 5.2x + 4y = 18 and 4x + 2y = 30 →
  6. 6.5x + 5y = −15 and x + 5y = −7 →
  7. 7.3x + 4y = 8 and 6x − 5y = −49 →
  8. 8.3x + 4y = 5 and 2x + y = 10 →
  9. 9.3x + 2y = 17 and 4x + y = 31 →
  10. 10.2x + 5y = 17 and 5x + 2y = 11 →
  11. 11.5x + y = 0 and 5x − 2y = 15 →
  12. 12.x − 6y = −27 and 4x − 4y = −28 →
  13. 13.6x + 3y = 21 and 4x + y = 9 →
  14. 14.2x + y = 19 and 4x + 3y = 43 →
  15. 15.4x − y = −11 and 2x + 2y = −28 →
  16. 16.3x + y = 19 and 4x + 2y = 24 →
  17. 17.8x + 5y = −6 and 5x + 8y = 6 →
  18. 18.6x + 4y = 70 and 2x + 2y = 26 →
  19. 19.2x + 2y = −10 and 3x − 3y = 39 →
  20. 20.x − 4y = 8 and 2x + 4y = 4 →
  21. 21.4x − 5y = 5 and 4x + 2y = 26 →
  22. 22.2x + 2y = 22 and 6x + 3y = 45 →
  23. 23.4x + 4y = 32 and 2x + 6y = 32 →
  24. 24.5x − y = 21 and x + y = 15 →
  25. 25.2x − 4y = 22 and 3x + y = 26 →
  26. 26.4x + 5y = −68 and 5x + 4y = −67 →
  27. 27.7x + y = 56 and x + 7y = 56 →
  28. 28.4x + 7y = −79 and 7x + 4y = −64 →
  29. 29.x − 2y = −8 and 3x − 2y = −20 →
  30. 30.x + 4y = −4 and 6x − 4y = 32 →
  31. 31.3x + 2y = 28 and 2x + 3y = 27 →
  32. 32.3x + y = 10 and 4x + 4y = 32 →
  33. 33.x + 4y = 19 and 6x − 2y = 10 →
  34. 34.5x + y = 23 and x + 5y = −5 →
  35. 35.5x + 2y = 14 and x − 6y = 22 →
  36. 36.x + 7y = −24 and 7x + y = 24 →
  37. 37.5x + y = 26 and 3x − 4y = 11 →
  38. 38.2x + 5y = 34 and 3x + y = 12 →
  39. 39.x + 8y = −60 and 8x + y = −39 →
  40. 40.x + 4y = −17 and 2x − y = −7 →

Answer key

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

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