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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 627 · 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.x + 3y = 13 and 2x − y = 12 →
  2. 2.x + 3y = 22 and 2x + 2y = 12 →
  3. 3.x + 5y = 32 and 5x + y = 16 →
  4. 4.5x + 3y = −21 and x + y = −5 →
  5. 5.2x − 2y = 2 and x + 4y = 31 →
  6. 6.x − 4y = −17 and 5x + 6y = 71 →
  7. 7.4x − 4y = 0 and x + y = 6 →
  8. 8.3x + 5y = 8 and 6x − 6y = 0 →
  9. 9.4x + 6y = −84 and 6x + 4y = −86 →
  10. 10.9x + 7y = 55 and 7x + 9y = 57 →
  11. 11.9x + 8y = 28 and 8x + 9y = 23 →
  12. 12.3x − y = 11 and 5x + 4y = 24 →
  13. 13.5x + 8y = 93 and 8x + 5y = 102 →
  14. 14.3x − 3y = 9 and x + 2y = 6 →
  15. 15.9x + 2y = −17 and 2x + 9y = 39 →
  16. 16.9x + 2y = 24 and 2x + 9y = 31 →
  17. 17.4x − y = 17 and 6x + y = 33 →
  18. 18.6x − 2y = 34 and 6x + 2y = 38 →
  19. 19.6x + 6y = 60 and 3x + 2y = 26 →
  20. 20.4x − 6y = −82 and x + 3y = 20 →
  21. 21.4x + 2y = 46 and 2x + 4y = 38 →
  22. 22.3x + 5y = −24 and 5x + 3y = −24 →
  23. 23.5x + 4y = −6 and 4x + 5y = −12 →
  24. 24.6x + 3y = −45 and 5x + 4y = −51 →
  25. 25.7x + 2y = −32 and 2x + 7y = −67 →
  26. 26.3x + 2y = −42 and 2x + 3y = −43 →
  27. 27.6x − 6y = −54 and x − 5y = −29 →
  28. 28.2x + 4y = 18 and 4x + 2y = 18 →
  29. 29.x + 3y = 25 and 5x − 2y = 23 →
  30. 30.2x − y = −15 and 3x + 4y = 5 →
  31. 31.3x + 6y = 15 and 4x + 2y = 2 →
  32. 32.2x + y = −2 and 4x − 2y = −12 →
  33. 33.x + 5y = −19 and 5x + 6y = 0 →
  34. 34.3x + 2y = 9 and 5x + 4y = 19 →
  35. 35.3x + 8y = −14 and 8x + 3y = 36 →
  36. 36.x − y = 0 and x + 3y = 32 →
  37. 37.6x + 6y = −6 and x + 2y = 0 →
  38. 38.x − 2y = −1 and x + 4y = 5 →
  39. 39.4x + 8y = −8 and 8x + 4y = −28 →
  40. 40.4x + 3y = 37 and 3x + 2y = 27 →

Answer key

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

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