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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 941 · 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 − 5y = −24 and 4x + y = 37 →
  2. 2.8x + 4y = 24 and 4x + 8y = 24 →
  3. 3.4x + 5y = 51 and 3x + 4y = 40 →
  4. 4.5x − 2y = −9 and x + 6y = −21 →
  5. 5.4x − y = 29 and 5x + 2y = 20 →
  6. 6.6x − 4y = −80 and x + y = 0 →
  7. 7.8x + 7y = −28 and 7x + 8y = −17 →
  8. 8.2x + y = −15 and 5x + 4y = −36 →
  9. 9.4x + 4y = 4 and 3x + 2y = −1 →
  10. 10.x + 4y = 5 and 4x − 3y = 1 →
  11. 11.5x + 6y = 32 and 6x + 5y = 34 →
  12. 12.3x + 6y = −57 and 2x + 6y = −54 →
  13. 13.4x + 5y = −32 and 5x + 4y = −31 →
  14. 14.5x + 4y = −32 and 6x − 5y = −58 →
  15. 15.3x + 6y = 36 and 2x + y = 3 →
  16. 16.x + 5y = 11 and 2x + 4y = 10 →
  17. 17.3x + 5y = 51 and 5x − 3y = −17 →
  18. 18.9x + 5y = 57 and 5x + 9y = 69 →
  19. 19.3x − y = 17 and 3x − 5y = 25 →
  20. 20.x − 4y = −30 and x + 2y = 24 →
  21. 21.x + y = 13 and x − 4y = −17 →
  22. 22.3x + 2y = 14 and 2x + 3y = 16 →
  23. 23.3x − 4y = 39 and 2x + 6y = −26 →
  24. 24.3x + 8y = 30 and 8x + 3y = 25 →
  25. 25.x − 2y = −4 and 3x + 6y = 24 →
  26. 26.6x + y = −17 and 2x + 5y = 27 →
  27. 27.9x + 8y = 76 and 8x + 9y = 77 →
  28. 28.2x − 6y = 62 and 3x + y = 3 →
  29. 29.2x + y = 1 and x + 5y = −4 →
  30. 30.x + y = 6 and 2x + y = 5 →
  31. 31.2x − 2y = −14 and 5x − 3y = −23 →
  32. 32.4x − 5y = 32 and 2x + 6y = −18 →
  33. 33.3x + 2y = 11 and 2x + y = 7 →
  34. 34.2x − 6y = −36 and 6x + 3y = 81 →
  35. 35.9x + 5y = 73 and 5x + 9y = 53 →
  36. 36.6x + 6y = −54 and 5x + 3y = −43 →
  37. 37.x + 5y = 3 and 6x + 3y = 45 →
  38. 38.9x + y = −9 and x + 9y = 79 →
  39. 39.3x − 4y = −15 and 6x − 3y = 0 →
  40. 40.6x + y = 38 and x + 3y = 12 →

Answer key

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

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