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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 865 · 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 + 6y = 3 and 6x + 3y = −3 →
  2. 2.7x + y = 54 and x + 7y = 42 →
  3. 3.4x + 3y = 48 and 3x + 4y = 43 →
  4. 4.4x + 2y = 30 and 5x + 5y = 60 →
  5. 5.6x + y = 38 and x + 6y = 18 →
  6. 6.8x + 2y = 42 and 2x + 8y = 18 →
  7. 7.6x + 2y = 60 and x + 3y = 26 →
  8. 8.3x + 2y = 18 and 6x + y = 18 →
  9. 9.2x + 5y = 12 and 5x + 2y = −12 →
  10. 10.x + 6y = 41 and 6x + y = 36 →
  11. 11.6x − 4y = 14 and 2x + y = 7 →
  12. 12.5x − 2y = −3 and 3x + 3y = 36 →
  13. 13.2x − 6y = −26 and 5x + 5y = 35 →
  14. 14.2x − y = 4 and 4x − 6y = 16 →
  15. 15.3x − 3y = −39 and 3x + 5y = −7 →
  16. 16.2x − y = −13 and 2x + 5y = 41 →
  17. 17.4x + 3y = 32 and 6x + y = 34 →
  18. 18.2x − 5y = −15 and 6x + 2y = 40 →
  19. 19.2x − 6y = −6 and 3x + 3y = 27 →
  20. 20.2x + 6y = 20 and 6x + 2y = 12 →
  21. 21.3x − 6y = 3 and 2x + 3y = 23 →
  22. 22.6x + 2y = −26 and 4x − y = −22 →
  23. 23.6x + 4y = −2 and 4x + 6y = −18 →
  24. 24.3x − 6y = −3 and 2x − y = −5 →
  25. 25.4x + 6y = 46 and 6x + 4y = 34 →
  26. 26.4x + 5y = 60 and 6x − 2y = 14 →
  27. 27.2x + 2y = 24 and 4x − 6y = −22 →
  28. 28.5x − 2y = 3 and x + 3y = 21 →
  29. 29.9x + 2y = 43 and 2x + 9y = 1 →
  30. 30.3x + 6y = −21 and 3x − 2y = 11 →
  31. 31.4x + 2y = 38 and 2x + 4y = 40 →
  32. 32.5x + y = −52 and 4x + y = −43 →
  33. 33.4x + 7y = −27 and 7x + 4y = −6 →
  34. 34.3x + 3y = 27 and 4x + 3y = 28 →
  35. 35.3x + 3y = 30 and 3x − y = 22 →
  36. 36.x + y = −5 and 3x + 4y = −11 →
  37. 37.5x + 4y = 16 and 4x + 5y = 2 →
  38. 38.5x − 5y = −15 and 5x + 2y = −36 →
  39. 39.x − 4y = 2 and 3x + 3y = 21 →
  40. 40.8x + 3y = 48 and 3x + 8y = 73 →

Answer key

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

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