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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 608 · 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. 1.3x + 8y = −57 and 8x + 3y = 13 →
  2. 2.2x + y = 22 and x + 2y = 20 →
  3. 3.5x + 6y = 51 and 6x + 5y = 48 →
  4. 4.5x + 4y = 49 and 5x + 2y = 47 →
  5. 5.6x − y = −62 and x + 2y = 7 →
  6. 6.4x + 5y = 17 and x − 5y = −2 →
  7. 7.5x + 3y = −32 and 6x + 6y = −36 →
  8. 8.x + 5y = −23 and 2x − 5y = 29 →
  9. 9.3x + 2y = −4 and x + 2y = −8 →
  10. 10.4x + 7y = −8 and 7x + 4y = 19 →
  11. 11.3x + 9y = 60 and 9x + 3y = 36 →
  12. 12.8x + y = 56 and x + 8y = 70 →
  13. 13.6x + y = 5 and 4x + 3y = −13 →
  14. 14.6x + 2y = 42 and 5x + 3y = 39 →
  15. 15.4x + y = −7 and x + 4y = −13 →
  16. 16.5x − 3y = 21 and 2x + 3y = 42 →
  17. 17.8x + 2y = −10 and 2x + 8y = −70 →
  18. 18.5x + 5y = 5 and 6x + 4y = −2 →
  19. 19.4x − 3y = 5 and 5x + 2y = 12 →
  20. 20.x + 2y = 19 and x + 5y = 46 →
  21. 21.3x + 6y = 63 and 6x + 3y = 54 →
  22. 22.6x + 4y = 40 and 4x + 6y = 40 →
  23. 23.4x + 5y = 0 and 4x − 6y = −44 →
  24. 24.5x + 5y = 60 and 3x + y = 28 →
  25. 25.5x − 6y = −3 and 6x + y = 62 →
  26. 26.2x + y = 7 and 2x + 5y = −5 →
  27. 27.6x + 6y = −18 and 6x + y = −48 →
  28. 28.x + 4y = −28 and 4x − y = 41 →
  29. 29.7x + 6y = −49 and 6x + 7y = −55 →
  30. 30.6x − 6y = −6 and 6x + 4y = 74 →
  31. 31.9x + y = 78 and x + 9y = 62 →
  32. 32.4x + 5y = −21 and 3x − 4y = −39 →
  33. 33.2x + 5y = −21 and 5x + 2y = 0 →
  34. 34.x − 2y = 8 and 2x + 4y = −8 →
  35. 35.x + y = −3 and 5x + y = 21 →
  36. 36.x − 6y = −25 and 5x − y = −9 →
  37. 37.3x + 2y = 10 and x + y = 6 →
  38. 38.4x + 4y = −8 and 3x + 4y = −4 →
  39. 39.4x + y = 25 and 4x + 4y = 28 →
  40. 40.5x + y = −36 and x + 5y = 36 →

Answer key

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

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