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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 525 · 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 + 5y = 32 and 5x + 6y = 65 →
  2. 2.7x + 8y = −34 and 8x + 7y = −26 →
  3. 3.2x + y = 15 and x + 2y = 15 →
  4. 4.2x − 2y = −4 and x + 5y = 52 →
  5. 5.3x + 3y = −45 and 2x + y = −21 →
  6. 6.6x − 5y = −27 and 3x + y = −3 →
  7. 7.4x − 6y = −58 and 2x + 2y = −4 →
  8. 8.7x + 3y = 45 and 3x + 7y = 65 →
  9. 9.7x + 9y = −13 and 9x + 7y = −3 →
  10. 10.2x − 5y = −3 and 6x + 5y = 11 →
  11. 11.2x + 6y = 26 and 6x + 2y = 30 →
  12. 12.2x − 5y = −31 and 6x + y = 19 →
  13. 13.6x + 8y = 90 and 8x + 6y = 92 →
  14. 14.3x − 3y = 15 and 4x + y = 30 →
  15. 15.4x − 4y = −12 and 4x + 3y = 16 →
  16. 16.9x + 2y = 29 and 2x + 9y = −62 →
  17. 17.2x + 2y = 18 and 4x + 6y = 38 →
  18. 18.x + 5y = 4 and 5x + y = 44 →
  19. 19.x + 7y = 34 and 7x + y = −50 →
  20. 20.2x + 5y = 20 and 3x + y = −9 →
  21. 21.9x + 7y = 22 and 7x + 9y = 42 →
  22. 22.4x + 9y = −18 and 9x + 4y = −73 →
  23. 23.2x + 4y = −24 and 4x + 2y = −36 →
  24. 24.3x − y = 5 and x + y = 11 →
  25. 25.5x + 6y = 11 and 6x + 5y = 11 →
  26. 26.5x + y = 35 and 4x + 3y = 39 →
  27. 27.6x + 5y = 26 and 4x + 3y = 16 →
  28. 28.2x + 6y = 30 and 3x − 6y = −60 →
  29. 29.x − 5y = −35 and 4x + 5y = 60 →
  30. 30.5x + 5y = 35 and 3x − 4y = 7 →
  31. 31.4x + 4y = −32 and 6x + y = −3 →
  32. 32.x + 5y = 24 and 5x + y = 24 →
  33. 33.6x + 3y = −27 and 3x + 6y = 27 →
  34. 34.x + 8y = 14 and 8x + y = −14 →
  35. 35.5x + 3y = 37 and 3x + 4y = 42 →
  36. 36.6x + y = 16 and 5x + 6y = 34 →
  37. 37.x + 2y = 15 and 2x + y = 9 →
  38. 38.4x + 6y = 66 and 6x − 2y = 44 →
  39. 39.2x + 2y = 20 and 2x + 5y = 47 →
  40. 40.x + 6y = 15 and 6x − 2y = 52 →

Answer key

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

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