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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 649 · 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. 1.2x + 6y = −8 and 6x + 4y = 32 →
  2. 2.3x − 4y = 47 and 4x + 3y = 21 →
  3. 3.x + 6y = 32 and x + 2y = 12 →
  4. 4.x + y = −5 and 5x + 4y = −23 →
  5. 5.x + 2y = 5 and 5x + 2y = −23 →
  6. 6.5x + 2y = 30 and 3x − 4y = 44 →
  7. 7.3x − y = 7 and x + 6y = 15 →
  8. 8.5x + 4y = 53 and x − y = 7 →
  9. 9.3x − 2y = −25 and 6x + y = −10 →
  10. 10.2x − 2y = −20 and 6x + 5y = 17 →
  11. 11.4x − 6y = −20 and 5x + y = −42 →
  12. 12.5x − 4y = −54 and 2x + 2y = 0 →
  13. 13.2x − 3y = −9 and 2x + 4y = −2 →
  14. 14.6x + 6y = 24 and 2x − 5y = −55 →
  15. 15.x + 3y = −16 and 5x − 4y = 15 →
  16. 16.x + y = 0 and x − 6y = −49 →
  17. 17.2x + 4y = −30 and 4x + 2y = −6 →
  18. 18.8x + 3y = 54 and 3x + 8y = 34 →
  19. 19.x + 5y = 21 and 5x − 2y = 24 →
  20. 20.x + 6y = 56 and 3x − 6y = −48 →
  21. 21.6x + 3y = 21 and 3x + 3y = 12 →
  22. 22.2x − 2y = 30 and 5x + y = 21 →
  23. 23.5x + 6y = 33 and 6x + 5y = 33 →
  24. 24.5x + 6y = 9 and 6x + 5y = −9 →
  25. 25.8x + 2y = 78 and 2x + 8y = 72 →
  26. 26.4x + 3y = 48 and 3x − 3y = −6 →
  27. 27.3x + y = −2 and 5x + 2y = −3 →
  28. 28.3x + 2y = 16 and 2x + 3y = 4 →
  29. 29.6x + y = −31 and 3x − 4y = −11 →
  30. 30.8x + 5y = 61 and 5x + 8y = 82 →
  31. 31.5x + 2y = 31 and x + y = 5 →
  32. 32.6x − 5y = −10 and 6x + y = −34 →
  33. 33.6x − 5y = 31 and 5x + 6y = 36 →
  34. 34.6x + 3y = 0 and 2x + 2y = 2 →
  35. 35.8x + 4y = 84 and 4x + 8y = 60 →
  36. 36.5x − 6y = 23 and 6x + 2y = 0 →
  37. 37.2x + 3y = −7 and 4x + 3y = −17 →
  38. 38.9x + 2y = 62 and 2x + 9y = 48 →
  39. 39.5x + 4y = 4 and x − 3y = 16 →
  40. 40.4x + 6y = 12 and 6x + 4y = −2 →

Answer key

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

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