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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 632 · 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 = −48 and 5x + 2y = −13 →
  2. 2.4x + 3y = −3 and 5x + 3y = 3 →
  3. 3.2x + y = −5 and x + 2y = −1 →
  4. 4.6x + 2y = −16 and 2x + 6y = −16 →
  5. 5.4x + 5y = 24 and 2x + 6y = 26 →
  6. 6.6x + y = 32 and 3x − 6y = 42 →
  7. 7.3x + 6y = −3 and 3x + 5y = −4 →
  8. 8.5x + 2y = 8 and x + 3y = 25 →
  9. 9.x + y = 6 and 2x + 5y = 15 →
  10. 10.4x + 5y = −4 and 3x + 5y = −8 →
  11. 11.5x + y = −2 and x + 5y = 14 →
  12. 12.5x − 2y = −29 and x + 6y = 7 →
  13. 13.4x + 6y = 14 and 4x + 5y = 17 →
  14. 14.x + y = 9 and 4x + 3y = 32 →
  15. 15.3x + y = 27 and 6x − 5y = 12 →
  16. 16.3x − 5y = 4 and 5x + 6y = 21 →
  17. 17.8x + 9y = 6 and 9x + 8y = 11 →
  18. 18.4x + 5y = 14 and 4x − y = 26 →
  19. 19.5x + 3y = 61 and 2x + 5y = 51 →
  20. 20.4x + 3y = 15 and 4x + 4y = 16 →
  21. 21.x + 7y = 66 and 7x + y = 30 →
  22. 22.x + 2y = 16 and 4x − 5y = 12 →
  23. 23.2x + 8y = 74 and 8x + 2y = 26 →
  24. 24.5x + 4y = 19 and 6x + 3y = 30 →
  25. 25.5x + 6y = 49 and 2x + 5y = 30 →
  26. 26.4x + y = −11 and x + 6y = 49 →
  27. 27.5x + 3y = 9 and 4x + 2y = 8 →
  28. 28.6x + y = 11 and 6x + 6y = 6 →
  29. 29.3x + 2y = 35 and 2x + 3y = 30 →
  30. 30.5x + 3y = −20 and 2x + 3y = −17 →
  31. 31.6x + 4y = −34 and 5x + y = −40 →
  32. 32.2x + 6y = 42 and x − y = 5 →
  33. 33.6x + 3y = 24 and 6x + 2y = 20 →
  34. 34.x + 2y = 6 and 2x + y = 6 →
  35. 35.4x + 3y = 51 and 3x + 4y = 54 →
  36. 36.7x + y = −44 and x + 7y = 28 →
  37. 37.2x + 5y = 21 and x + 4y = 18 →
  38. 38.8x + 3y = 54 and 3x + 8y = 34 →
  39. 39.6x − 3y = −24 and 4x + 3y = −6 →
  40. 40.2x + 4y = 32 and 4x + 2y = 40 →

Answer key

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

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