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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 364 · 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. 1.6x − 5y = 34 and 6x + y = 58 →
  2. 2.3x + 6y = −57 and 6x − y = 3 →
  3. 3.3x + 5y = −16 and 5x − 2y = −37 →
  4. 4.x + 3y = −22 and 3x + y = −10 →
  5. 5.7x + 6y = 4 and 6x + 7y = 9 →
  6. 6.3x − 3y = 0 and 5x − 3y = 2 →
  7. 7.x + 5y = 19 and x + 6y = 21 →
  8. 8.x + 6y = 1 and 2x + 5y = 9 →
  9. 9.4x − y = 33 and 4x − 5y = 21 →
  10. 10.3x − 2y = 25 and 2x + 3y = 21 →
  11. 11.x + 3y = 7 and 3x + y = 5 →
  12. 12.7x + 4y = 3 and 4x + 7y = −36 →
  13. 13.8x + 5y = 29 and 5x + 8y = −16 →
  14. 14.x + 6y = 12 and 3x + y = −15 →
  15. 15.x + 5y = −34 and 5x + y = 22 →
  16. 16.6x − 6y = 36 and 5x + 5y = 50 →
  17. 17.4x − 2y = −46 and 2x + 2y = 4 →
  18. 18.4x + y = 37 and x + 2y = 11 →
  19. 19.2x − 6y = −16 and 5x + 3y = 32 →
  20. 20.5x + 4y = −10 and 5x + 3y = −5 →
  21. 21.x − 6y = −34 and x − 5y = −27 →
  22. 22.6x + y = 10 and 6x + 6y = 0 →
  23. 23.x − 4y = −39 and 4x + 6y = 42 →
  24. 24.6x − 2y = −30 and 5x − 5y = −35 →
  25. 25.4x + 9y = 31 and 9x + 4y = 21 →
  26. 26.3x − 3y = −36 and 2x + 3y = 21 →
  27. 27.4x + 6y = −10 and 6x + 5y = 13 →
  28. 28.x + 9y = −83 and 9x + y = −27 →
  29. 29.5x − 4y = 47 and 3x + 6y = −39 →
  30. 30.6x + 2y = 22 and 3x + 2y = 10 →
  31. 31.5x + 7y = 26 and 7x + 5y = 46 →
  32. 32.5x + 8y = −42 and 8x + 5y = 3 →
  33. 33.9x + 3y = 48 and 3x + 9y = 24 →
  34. 34.5x − y = −1 and 5x + 4y = 29 →
  35. 35.2x + 4y = 20 and x + y = 9 →
  36. 36.5x + 6y = 23 and 6x + 5y = 32 →
  37. 37.x + 7y = −9 and 7x + y = 33 →
  38. 38.4x + y = 32 and 6x + 4y = 58 →
  39. 39.9x + 4y = −30 and 4x + 9y = −35 →
  40. 40.5x − 5y = −20 and 5x − y = −40 →

Answer key

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

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