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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 71 · 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 = −42 and 5x + 2y = 26 →
  2. 2.x + 3y = 8 and 6x − 3y = 6 →
  3. 3.x + 4y = 36 and x + y = 15 →
  4. 4.8x + 5y = 16 and 5x + 8y = −29 →
  5. 5.4x + 3y = −33 and 3x − 4y = 19 →
  6. 6.2x − 3y = −20 and 4x + 3y = −4 →
  7. 7.5x + y = −33 and 3x + 5y = −11 →
  8. 8.8x + 3y = −70 and 3x + 8y = −40 →
  9. 9.9x + 5y = 101 and 5x + 9y = 81 →
  10. 10.3x + 3y = 3 and 4x − 3y = −10 →
  11. 11.5x + 2y = 51 and 2x + 5y = 33 →
  12. 12.8x + y = 73 and x + 8y = 17 →
  13. 13.x + 3y = −5 and 5x + 5y = −15 →
  14. 14.6x + 8y = 62 and 8x + 6y = 64 →
  15. 15.5x + 6y = −3 and x + y = −1 →
  16. 16.5x + 2y = 22 and 4x + y = 14 →
  17. 17.5x + 6y = 51 and 6x + 6y = 60 →
  18. 18.2x − y = −7 and x − 5y = 37 →
  19. 19.6x + y = 19 and 3x + 5y = −13 →
  20. 20.3x − 6y = −54 and 6x − y = −20 →
  21. 21.6x + 3y = 63 and x − 5y = −6 →
  22. 22.6x − 3y = −6 and 4x + 6y = 44 →
  23. 23.2x + y = 13 and x − y = −1 →
  24. 24.9x + 3y = 33 and 3x + 9y = 27 →
  25. 25.6x + 2y = 16 and x + 5y = 26 →
  26. 26.8x + 6y = 12 and 6x + 8y = −12 →
  27. 27.6x + 4y = 42 and 4x + 6y = 58 →
  28. 28.2x + 9y = −33 and 9x + 2y = 44 →
  29. 29.9x + 3y = 24 and 3x + 9y = 24 →
  30. 30.x + 3y = 15 and 2x − 4y = 10 →
  31. 31.2x + 6y = −40 and 5x + 3y = −16 →
  32. 32.6x + 7y = −103 and 7x + 6y = −105 →
  33. 33.5x + 3y = 19 and 4x − 3y = 26 →
  34. 34.4x + 3y = 5 and 3x + 4y = 2 →
  35. 35.6x + 6y = 84 and 6x − 2y = 44 →
  36. 36.x + 6y = −37 and x − 4y = 23 →
  37. 37.x − y = −1 and 4x + 4y = 28 →
  38. 38.3x − 2y = −6 and x + 3y = 31 →
  39. 39.5x + 2y = 47 and 4x − 6y = −8 →
  40. 40.2x − 3y = −3 and x − 6y = −24 →

Answer key

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

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