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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 735 · 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. 1.2x − y = 8 and 2x + y = 12 →
  2. 2.x + 3y = 10 and x + 5y = 18 →
  3. 3.4x + 3y = 19 and 2x + 6y = 50 →
  4. 4.2x + y = 15 and x + y = 8 →
  5. 5.8x + 4y = 44 and 4x + 8y = 16 →
  6. 6.2x − 4y = −16 and 5x + 2y = 44 →
  7. 7.7x + 2y = −12 and 2x + 7y = 3 →
  8. 8.x + 6y = 13 and 5x + 6y = 41 →
  9. 9.2x + 3y = −1 and 3x + 3y = −6 →
  10. 10.3x − 3y = 15 and 3x − 2y = 19 →
  11. 11.2x − y = 7 and 4x − y = 15 →
  12. 12.6x − 3y = −36 and 5x + 6y = 38 →
  13. 13.x + 9y = 42 and 9x + y = −22 →
  14. 14.2x + 8y = 38 and 8x + 2y = −58 →
  15. 15.2x − y = 3 and 2x − 4y = −6 →
  16. 16.6x + 8y = −10 and 8x + 6y = −18 →
  17. 17.2x + 3y = 5 and x + 2y = 4 →
  18. 18.2x + 8y = −26 and 8x + 2y = 46 →
  19. 19.3x + 8y = 30 and 8x + 3y = 25 →
  20. 20.2x + 6y = 34 and 3x + 2y = 9 →
  21. 21.3x + 3y = −21 and 3x − 6y = −30 →
  22. 22.2x + 7y = 16 and 7x + 2y = 11 →
  23. 23.3x − 2y = 13 and 2x − y = 11 →
  24. 24.x + 4y = 13 and 6x − 5y = −9 →
  25. 25.4x + 3y = 30 and x − y = −3 →
  26. 26.4x + 3y = 43 and 4x + 6y = 58 →
  27. 27.x + 6y = 22 and 6x + y = 27 →
  28. 28.6x + 4y = −52 and x − 3y = −5 →
  29. 29.x − 5y = 23 and 4x − 3y = −10 →
  30. 30.4x + 8y = 84 and 8x + 4y = 60 →
  31. 31.x − y = −2 and 4x + 2y = 22 →
  32. 32.2x + 2y = −24 and x + 2y = −16 →
  33. 33.3x − 4y = −57 and x + y = 2 →
  34. 34.2x − 2y = 10 and 2x + 6y = 26 →
  35. 35.x + 5y = 13 and 2x − y = 15 →
  36. 36.3x + 2y = 33 and 2x + 3y = 37 →
  37. 37.5x + 3y = 51 and 3x + 5y = 37 →
  38. 38.2x + 2y = 32 and 6x + 3y = 69 →
  39. 39.2x + 7y = −42 and 7x + 2y = 33 →
  40. 40.x − 3y = −20 and 4x + 2y = 32 →

Answer key

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

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