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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 266 · 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 − 2y = 33 and 6x + 4y = −6 →
  2. 2.4x + 2y = 46 and 2x + 4y = 50 →
  3. 3.5x − 3y = 24 and 2x − y = 10 →
  4. 4.x + 4y = −19 and 5x + 5y = −50 →
  5. 5.x − 2y = −4 and 6x + 4y = 40 →
  6. 6.5x − 5y = 5 and 3x + 6y = −15 →
  7. 7.4x + 3y = 29 and 3x + 4y = 27 →
  8. 8.5x + 4y = 37 and 4x + 5y = 26 →
  9. 9.6x + 2y = −26 and x − 4y = −39 →
  10. 10.6x + 7y = 41 and 7x + 6y = 37 →
  11. 11.4x + 5y = −22 and 3x + 3y = −12 →
  12. 12.5x + y = −3 and x + 5y = 9 →
  13. 13.7x + 9y = 17 and 9x + 7y = 31 →
  14. 14.6x − 3y = −27 and 3x + 6y = 24 →
  15. 15.2x + 5y = −25 and 3x + 4y = −13 →
  16. 16.9x + 4y = −46 and 4x + 9y = −6 →
  17. 17.3x + 9y = −48 and 9x + 3y = 24 →
  18. 18.4x + 2y = −40 and 3x + 2y = −31 →
  19. 19.9x + 8y = −90 and 8x + 9y = −97 →
  20. 20.5x − 4y = 30 and 6x + 3y = −3 →
  21. 21.3x − 6y = −12 and 3x + 2y = −4 →
  22. 22.6x + y = 39 and x + 6y = 24 →
  23. 23.x + 9y = 47 and 9x + y = −57 →
  24. 24.3x + 6y = −42 and 6x + 3y = −3 →
  25. 25.2x + 5y = −33 and 6x + 2y = −60 →
  26. 26.6x + 2y = −16 and 4x − 3y = −28 →
  27. 27.8x + 9y = −29 and 9x + 8y = −39 →
  28. 28.4x + 6y = 36 and 6x + 4y = 34 →
  29. 29.2x + 2y = 8 and 2x − 5y = 1 →
  30. 30.5x − 6y = 40 and x + 2y = −8 →
  31. 31.2x + 6y = −46 and 6x + 5y = −34 →
  32. 32.x − 2y = 2 and 3x − 3y = −9 →
  33. 33.2x + 4y = 2 and 5x + 5y = −15 →
  34. 34.3x + y = 23 and x + 3y = 21 →
  35. 35.5x − 4y = 63 and 5x + 6y = −7 →
  36. 36.6x + 7y = 66 and 7x + 6y = 64 →
  37. 37.x + 2y = −13 and 5x + 6y = −53 →
  38. 38.6x + 3y = 57 and x + 4y = 13 →
  39. 39.6x + 8y = 78 and 8x + 6y = 62 →
  40. 40.x + 6y = 24 and 4x + 6y = 6 →

Answer key

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

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