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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 44 · 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 + 8y = 31 and 8x + y = 59 →
  2. 2.5x + 2y = 41 and 5x − 6y = 57 →
  3. 3.2x + y = 1 and x + 2y = 8 →
  4. 4.8x + 5y = 23 and 5x + 8y = −10 →
  5. 5.2x + 9y = −52 and 9x + 2y = −80 →
  6. 6.5x + 7y = 19 and 7x + 5y = 17 →
  7. 7.6x + 7y = 39 and 7x + 6y = 39 →
  8. 8.6x − 6y = 18 and x − 3y = −9 →
  9. 9.4x − 4y = −64 and 6x + 3y = −33 →
  10. 10.x + 5y = 16 and 6x − 5y = −44 →
  11. 11.x + 4y = −20 and x + 2y = −6 →
  12. 12.2x + 8y = 64 and 8x + 2y = 46 →
  13. 13.4x + 2y = −10 and x + 5y = 20 →
  14. 14.5x + 3y = −19 and 4x + 5y = −36 →
  15. 15.4x + 2y = 48 and 5x + 5y = 75 →
  16. 16.7x + 4y = −18 and 4x + 7y = 18 →
  17. 17.4x + 6y = −18 and x + 3y = −15 →
  18. 18.6x + 9y = −30 and 9x + 6y = −30 →
  19. 19.x + 5y = 36 and 6x + y = 42 →
  20. 20.x + 6y = 22 and 6x + y = 27 →
  21. 21.8x + 6y = 26 and 6x + 8y = 2 →
  22. 22.x + 5y = 37 and 5x − 3y = 17 →
  23. 23.9x + 6y = −51 and 6x + 9y = −9 →
  24. 24.8x + 3y = 78 and 3x + 8y = 43 →
  25. 25.4x + y = −28 and 6x + 2y = −40 →
  26. 26.7x + 9y = −78 and 9x + 7y = −82 →
  27. 27.5x − 6y = −93 and 4x − 5y = −76 →
  28. 28.2x + 4y = 28 and 2x + 3y = 25 →
  29. 29.4x + 6y = 78 and x + 2y = 24 →
  30. 30.x − 4y = −9 and 3x + 3y = −12 →
  31. 31.6x + 6y = 30 and 2x + 5y = 19 →
  32. 32.x + 5y = 13 and 5x + y = 17 →
  33. 33.6x + 7y = 99 and 7x + 6y = 96 →
  34. 34.5x + 3y = −43 and x − 5y = 25 →
  35. 35.4x + 5y = 6 and 6x + 5y = 4 →
  36. 36.5x + 5y = 60 and 6x + 4y = 54 →
  37. 37.6x + 2y = 54 and 2x + 2y = 26 →
  38. 38.8x + 4y = −48 and 4x + 8y = 0 →
  39. 39.4x + y = −36 and x + 4y = −24 →
  40. 40.4x + y = 29 and x + 4y = −4 →

Answer key

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

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