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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 480 · 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 − 4y = −29 and 3x − 5y = −37 →
  2. 2.3x + 3y = −15 and 5x + y = 3 →
  3. 3.4x + 4y = 60 and 3x + 5y = 59 →
  4. 4.9x + 3y = 15 and 3x + 9y = −27 →
  5. 5.5x + 4y = 36 and 4x + 5y = 36 →
  6. 6.4x + 3y = 0 and 2x − 4y = 22 →
  7. 7.4x + 4y = 56 and 3x − y = 22 →
  8. 8.8x + 5y = 57 and 5x + 8y = 60 →
  9. 9.x + 2y = −10 and 3x + 5y = −24 →
  10. 10.6x + 7y = −13 and 7x + 6y = 0 →
  11. 11.x + 5y = 0 and x − 2y = 7 →
  12. 12.2x + y = 18 and 6x + 5y = 66 →
  13. 13.2x + y = 5 and 2x + 5y = 1 →
  14. 14.3x + y = 27 and x − 3y = −1 →
  15. 15.2x + 6y = 34 and 6x + 2y = −26 →
  16. 16.3x + y = 6 and x + 3y = −22 →
  17. 17.4x + y = −7 and 4x − 3y = −27 →
  18. 18.4x − 2y = 0 and 6x − 4y = −2 →
  19. 19.6x + 3y = 63 and x + 2y = 21 →
  20. 20.2x + 5y = −12 and 5x + 2y = −9 →
  21. 21.8x + 3y = 19 and 3x + 8y = −41 →
  22. 22.x − 3y = 13 and 4x + y = 26 →
  23. 23.x + 2y = 0 and 2x + y = −3 →
  24. 24.3x + y = −13 and x + 3y = −15 →
  25. 25.2x − 5y = 19 and 4x + 6y = −10 →
  26. 26.2x − y = −2 and 6x + 2y = 24 →
  27. 27.x − 5y = −34 and 3x + 4y = 50 →
  28. 28.2x + y = −16 and 5x + y = −37 →
  29. 29.3x + y = −16 and 5x + 5y = −20 →
  30. 30.x − 2y = −11 and 4x + y = 37 →
  31. 31.5x + 5y = 0 and 5x + 2y = 3 →
  32. 32.x + 6y = −41 and 6x + y = −1 →
  33. 33.4x + 6y = 48 and 6x + 4y = 62 →
  34. 34.5x − 2y = 2 and 5x + 2y = 18 →
  35. 35.4x + 4y = −4 and x + 3y = 7 →
  36. 36.4x + 3y = −1 and 6x + y = 23 →
  37. 37.x + 8y = −8 and 8x + y = 62 →
  38. 38.2x + 8y = 44 and 8x + 2y = −4 →
  39. 39.4x + y = 30 and x + 4y = 0 →
  40. 40.2x + y = 12 and 3x + 4y = 38 →

Answer key

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

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