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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 514 · 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 + 3y = 3 and 6x − y = 62 →
  2. 2.x + 4y = 8 and x + 2y = 6 →
  3. 3.5x + 3y = 19 and 2x + 6y = −26 →
  4. 4.3x + 3y = 27 and 2x + 3y = 20 →
  5. 5.x + 2y = 3 and 3x + 4y = 7 →
  6. 6.6x + 2y = −68 and 4x − 3y = −15 →
  7. 7.6x − 4y = −70 and x − 3y = −21 →
  8. 8.2x + 2y = 4 and 4x + y = 26 →
  9. 9.x + 2y = 12 and 2x − 5y = 6 →
  10. 10.x + 6y = −50 and 6x + 3y = −3 →
  11. 11.2x + 3y = 0 and 3x + 2y = 15 →
  12. 12.x + 4y = 25 and 5x + 6y = 41 →
  13. 13.2x − 3y = 6 and x + 3y = 21 →
  14. 14.x + 6y = 38 and 2x + 5y = 41 →
  15. 15.4x − 4y = −4 and x + 2y = −19 →
  16. 16.3x + 2y = 5 and x − 3y = −2 →
  17. 17.2x + 7y = 37 and 7x + 2y = 62 →
  18. 18.5x + 5y = 30 and 2x − 5y = −2 →
  19. 19.7x + y = 24 and x + 7y = 24 →
  20. 20.4x + y = 5 and x + 6y = 7 →
  21. 21.7x + 9y = 119 and 9x + 7y = 121 →
  22. 22.5x + 5y = 20 and 4x + 6y = 28 →
  23. 23.3x − 6y = 33 and 6x + 6y = 48 →
  24. 24.3x + 5y = 2 and 3x + y = −14 →
  25. 25.6x + 6y = −66 and 2x + y = −18 →
  26. 26.4x − 6y = −6 and 2x − 2y = 0 →
  27. 27.9x + 8y = 17 and 8x + 9y = 17 →
  28. 28.3x − 5y = 44 and x + 3y = −4 →
  29. 29.6x + 3y = 69 and 3x + 6y = 57 →
  30. 30.6x + 7y = 13 and 7x + 6y = 13 →
  31. 31.4x + 5y = 22 and 3x + 6y = 21 →
  32. 32.5x + 8y = 68 and 8x + 5y = 62 →
  33. 33.5x + 6y = 39 and x + 2y = 15 →
  34. 34.2x + 3y = −31 and 5x − 3y = 17 →
  35. 35.4x + 6y = −12 and 5x − 4y = 54 →
  36. 36.7x + 9y = −13 and 9x + 7y = −35 →
  37. 37.2x + y = 22 and 5x − 2y = 19 →
  38. 38.x + 4y = −5 and 4x − y = −37 →
  39. 39.5x − 6y = 52 and 4x + 2y = 28 →
  40. 40.x + 2y = 24 and 3x + 2y = 36 →

Answer key

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

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