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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 716 · 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. 1.5x + y = 8 and x + 5y = −32 →
  2. 2.2x + 7y = 45 and 7x + 2y = 0 →
  3. 3.2x + 9y = −2 and 9x + 2y = 68 →
  4. 4.3x + 6y = 3 and 4x − 3y = −29 →
  5. 5.x + y = 2 and 6x + 3y = −9 →
  6. 6.6x + 3y = −30 and 4x − 4y = −68 →
  7. 7.x − 2y = −11 and 2x − 5y = −28 →
  8. 8.7x + 4y = −23 and 4x + 7y = −32 →
  9. 9.6x + 4y = 22 and 4x + y = 8 →
  10. 10.3x + 5y = 45 and x − 5y = −25 →
  11. 11.6x + 4y = 82 and x + 5y = 44 →
  12. 12.4x + y = 23 and x + 2y = −3 →
  13. 13.2x − 3y = 29 and 4x − 5y = 49 →
  14. 14.5x + y = −26 and 3x + 2y = −10 →
  15. 15.7x + 4y = 47 and 4x + 7y = 8 →
  16. 16.2x + y = 13 and x + 2y = 17 →
  17. 17.x + 6y = −4 and 6x + y = 11 →
  18. 18.3x − 2y = 36 and x + 4y = −30 →
  19. 19.2x + 6y = 16 and x + 2y = 7 →
  20. 20.2x + 6y = 18 and 3x + 2y = 20 →
  21. 21.3x + 3y = 33 and 2x + y = 20 →
  22. 22.4x + y = 22 and 5x + 3y = 24 →
  23. 23.3x + 6y = −33 and 2x − 6y = −2 →
  24. 24.x − 2y = −18 and x + 3y = 22 →
  25. 25.4x + 3y = 20 and 4x − 3y = 44 →
  26. 26.6x − 6y = 60 and 5x + 4y = −13 →
  27. 27.2x + 6y = 40 and 6x + 2y = −24 →
  28. 28.8x + 7y = −50 and 7x + 8y = −40 →
  29. 29.5x + 5y = 75 and 5x + 3y = 61 →
  30. 30.5x + 5y = 20 and x + 6y = 14 →
  31. 31.5x + 2y = 40 and 2x − 6y = −18 →
  32. 32.x + 2y = 4 and 2x + y = 11 →
  33. 33.2x + 2y = 10 and 3x + 6y = 33 →
  34. 34.3x − 3y = −24 and 3x − y = −22 →
  35. 35.2x + 3y = 27 and 2x − 3y = −15 →
  36. 36.4x − 3y = 35 and 3x + y = −3 →
  37. 37.5x + 2y = −3 and 2x + 5y = 3 →
  38. 38.3x + 4y = −1 and x + 6y = −5 →
  39. 39.3x − 5y = 25 and x − 5y = 15 →
  40. 40.6x + y = −11 and 4x + 5y = −3 →

Answer key

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

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