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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 339 · 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 + 3y = 3 and x + 2y = 8 →
  2. 2.2x − 2y = 0 and 3x + 4y = −7 →
  3. 3.6x + 2y = 24 and 5x + 5y = 30 →
  4. 4.2x − 3y = 21 and 2x − 6y = 24 →
  5. 5.6x + 7y = 0 and 7x + 6y = 13 →
  6. 6.2x + 2y = 0 and 2x + y = 5 →
  7. 7.3x + 5y = 62 and 5x + 3y = 66 →
  8. 8.2x + y = 25 and x + 2y = 26 →
  9. 9.4x + 8y = 100 and 8x + 4y = 92 →
  10. 10.4x + 4y = 28 and 4x − 6y = −52 →
  11. 11.4x + 4y = 16 and 3x − 6y = 3 →
  12. 12.3x − y = 7 and 6x − 5y = 17 →
  13. 13.x + 5y = −24 and 5x + y = −48 →
  14. 14.6x − y = 10 and x + y = −3 →
  15. 15.8x + y = 60 and x + 8y = 39 →
  16. 16.x + 2y = 20 and 2x + y = 19 →
  17. 17.2x + 4y = −20 and 5x + 4y = −2 →
  18. 18.4x + 5y = 14 and x + y = 4 →
  19. 19.6x + 5y = 22 and 5x + 6y = 22 →
  20. 20.3x − y = 21 and 2x + 4y = 28 →
  21. 21.x + 4y = 5 and 6x + 6y = 48 →
  22. 22.2x + 5y = 31 and 5x + 3y = 30 →
  23. 23.6x + 7y = −5 and 7x + 6y = −8 →
  24. 24.x + 6y = 35 and 4x + 4y = 40 →
  25. 25.2x + 3y = 28 and 5x + 4y = 49 →
  26. 26.9x + 7y = 70 and 7x + 9y = 58 →
  27. 27.4x + 2y = −10 and 2x + 4y = 22 →
  28. 28.5x + y = 37 and 2x + y = 19 →
  29. 29.6x + 4y = 38 and 5x − 2y = −11 →
  30. 30.2x + y = 5 and 4x + 5y = −5 →
  31. 31.6x − 5y = −76 and 2x + 5y = 28 →
  32. 32.3x + 2y = 19 and 4x + 4y = 36 →
  33. 33.9x + 7y = 26 and 7x + 9y = 38 →
  34. 34.3x + 9y = 63 and 9x + 3y = 93 →
  35. 35.4x + 2y = −4 and 2x + 4y = 4 →
  36. 36.x + y = 7 and 6x − y = 35 →
  37. 37.x − 5y = −27 and 6x − 4y = 20 →
  38. 38.5x + 5y = 50 and x + 2y = 14 →
  39. 39.x + 6y = −6 and 2x + 6y = 0 →
  40. 40.5x + 2y = 22 and 4x + 6y = 22 →

Answer key

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

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