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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 758 · 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 + 9y = 41 and 9x + y = 49 →
  2. 2.2x + 5y = 23 and 3x − y = 26 →
  3. 3.8x + 5y = −67 and 5x + 8y = −76 →
  4. 4.2x + 6y = 48 and 6x + 2y = 64 →
  5. 5.2x − 6y = −2 and x + 2y = 14 →
  6. 6.4x + 4y = 12 and 2x + 3y = 7 →
  7. 7.7x + 3y = −31 and 3x + 7y = −59 →
  8. 8.3x + 3y = 18 and x + 4y = 21 →
  9. 9.x + 4y = −27 and 2x + y = −19 →
  10. 10.5x + y = 15 and 5x + 4y = 30 →
  11. 11.6x + 5y = 4 and 4x − 5y = −64 →
  12. 12.6x − 4y = 18 and 6x + 3y = 39 →
  13. 13.2x − y = 1 and 6x − 2y = 4 →
  14. 14.4x + 4y = 44 and 3x + 5y = 43 →
  15. 15.4x + 4y = 64 and 3x + 4y = 55 →
  16. 16.x + 4y = 20 and 3x + 2y = 0 →
  17. 17.4x − 3y = −32 and x − 5y = −25 →
  18. 18.3x − 3y = −6 and 3x + y = 22 →
  19. 19.3x + 3y = −24 and 2x + y = −11 →
  20. 20.2x + 4y = 44 and 4x + 2y = 46 →
  21. 21.4x + 5y = −23 and 4x + 3y = −25 →
  22. 22.7x + 6y = 38 and 6x + 7y = 40 →
  23. 23.6x + 2y = 70 and 2x + 6y = 66 →
  24. 24.3x + y = −26 and 3x + 6y = −51 →
  25. 25.4x + 5y = −49 and x + y = −11 →
  26. 26.5x + 6y = −24 and 6x + 5y = −31 →
  27. 27.5x + 2y = −36 and 2x + 5y = −6 →
  28. 28.4x + 2y = −20 and 2x + 4y = 8 →
  29. 29.3x + 7y = −57 and 7x + 3y = −53 →
  30. 30.3x + 5y = 64 and 4x − 2y = 16 →
  31. 31.2x + 2y = −6 and 5x + 2y = 9 →
  32. 32.4x + 2y = 28 and x + 5y = 34 →
  33. 33.2x + 6y = −14 and 6x + 2y = 6 →
  34. 34.6x + y = 9 and 3x + 5y = 18 →
  35. 35.8x + 9y = −1 and 9x + 8y = −16 →
  36. 36.2x + y = 3 and 6x + 2y = 10 →
  37. 37.4x − 2y = −32 and 4x − y = −24 →
  38. 38.9x + 6y = 108 and 6x + 9y = 117 →
  39. 39.4x − 5y = 66 and x − 4y = 33 →
  40. 40.3x + y = 27 and 2x − 2y = −6 →

Answer key

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

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