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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 628 · 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. 1.5x + 3y = 33 and 3x + 5y = 7 →
  2. 2.2x + 4y = 34 and 6x − 2y = −24 →
  3. 3.5x + 4y = 6 and 3x + 4y = 10 →
  4. 4.x + 5y = 15 and 4x + 4y = 28 →
  5. 5.x + 5y = 32 and 3x + 3y = 36 →
  6. 6.2x − 6y = 58 and 2x + y = −5 →
  7. 7.7x + 3y = −8 and 3x + 7y = 48 →
  8. 8.5x − 2y = 43 and 4x + 3y = 39 →
  9. 9.x + 6y = −23 and 6x + 2y = −2 →
  10. 10.5x − 2y = 36 and 5x + y = 42 →
  11. 11.x + 5y = −24 and 4x + 4y = −16 →
  12. 12.5x − 4y = −44 and 4x + 6y = −26 →
  13. 13.x + y = 11 and 5x − 3y = −17 →
  14. 14.x + 2y = 2 and 2x + y = −8 →
  15. 15.3x + 3y = 6 and 3x + 4y = 5 →
  16. 16.2x − 4y = −10 and 5x + 6y = 55 →
  17. 17.3x − 3y = 0 and 6x + 5y = −11 →
  18. 18.x + y = 8 and 2x + 6y = 36 →
  19. 19.x + 2y = 6 and 4x + 6y = 20 →
  20. 20.3x + 2y = 19 and 5x + 5y = 35 →
  21. 21.5x + 9y = −48 and 9x + 5y = −8 →
  22. 22.7x + 6y = 47 and 6x + 7y = 44 →
  23. 23.4x + 7y = 46 and 7x + 4y = 31 →
  24. 24.7x + 6y = 34 and 6x + 7y = 31 →
  25. 25.7x + 2y = 54 and 2x + 7y = 54 →
  26. 26.6x − 5y = 7 and 5x + 2y = −25 →
  27. 27.2x + 2y = −6 and 2x + 4y = −24 →
  28. 28.6x + 3y = 0 and 3x + 6y = 27 →
  29. 29.3x − 5y = −16 and 4x + 3y = −2 →
  30. 30.4x + 4y = 36 and 6x − 6y = 6 →
  31. 31.2x + 7y = 67 and 7x + 2y = 32 →
  32. 32.4x + 5y = 26 and 3x − 6y = 0 →
  33. 33.x + 2y = −5 and 3x − 2y = 1 →
  34. 34.5x + 6y = −48 and 6x + 5y = −51 →
  35. 35.4x + 4y = 24 and x + 6y = 16 →
  36. 36.7x + 6y = 68 and 6x + 7y = 75 →
  37. 37.4x + 9y = 67 and 9x + 4y = 37 →
  38. 38.x + 8y = 46 and 8x + y = 53 →
  39. 39.5x − 4y = 7 and 3x + 2y = 13 →
  40. 40.5x + 5y = −20 and 5x − 4y = 61 →

Answer key

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

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