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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 154 · 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 + 5y = 9 and 2x + y = 13 →
  2. 2.5x + 5y = 45 and 6x + 3y = 36 →
  3. 3.3x + 3y = 45 and 4x − 2y = 12 →
  4. 4.2x + y = 11 and 5x − 6y = 53 →
  5. 5.2x − 3y = 34 and 6x − 5y = 78 →
  6. 6.x − 2y = 10 and 5x + y = −38 →
  7. 7.5x − y = 22 and 2x + 4y = 44 →
  8. 8.x + 7y = 60 and 7x + y = 36 →
  9. 9.4x − 3y = 2 and 3x − y = −1 →
  10. 10.2x + 9y = −20 and 9x + 2y = −13 →
  11. 11.6x + y = 7 and 6x + 5y = 11 →
  12. 12.4x + 2y = −16 and x + 4y = −11 →
  13. 13.5x + y = 7 and x + 5y = 11 →
  14. 14.x + 6y = 14 and x − 3y = −13 →
  15. 15.5x + 6y = −18 and 6x + 5y = −4 →
  16. 16.x + y = 14 and 5x + 2y = 46 →
  17. 17.2x − 5y = −13 and 2x + 2y = −6 →
  18. 18.2x + 5y = −34 and 5x + 2y = −1 →
  19. 19.6x + 2y = −54 and 2x + 6y = −66 →
  20. 20.x + 4y = 35 and 6x − 2y = 28 →
  21. 21.4x + 9y = 42 and 9x + 4y = −3 →
  22. 22.4x + 6y = 74 and 6x + 4y = 76 →
  23. 23.5x + 3y = −2 and 2x + y = 0 →
  24. 24.4x + 3y = −42 and 3x + 4y = −42 →
  25. 25.3x + 7y = −56 and 7x + 3y = −64 →
  26. 26.4x + 6y = 16 and 6x + 4y = 14 →
  27. 27.3x + 8y = −61 and 8x + 3y = −71 →
  28. 28.5x + 3y = 23 and 3x + 5y = 33 →
  29. 29.x + 3y = 16 and 6x − y = 1 →
  30. 30.2x + 6y = 14 and 6x + 5y = 29 →
  31. 31.2x + y = 11 and x + 2y = 16 →
  32. 32.6x + 6y = 54 and 2x + 6y = 34 →
  33. 33.2x + 3y = 39 and 3x + 2y = 41 →
  34. 34.7x + 2y = 47 and 2x + 7y = 7 →
  35. 35.6x + 8y = 4 and 8x + 6y = 10 →
  36. 36.7x + 3y = 5 and 3x + 7y = 25 →
  37. 37.3x + 8y = 3 and 8x + 3y = 63 →
  38. 38.3x + 5y = 37 and 5x + 3y = 35 →
  39. 39.9x + 4y = −53 and 4x + 9y = 27 →
  40. 40.6x + 4y = 2 and 6x − 5y = 11 →

Answer key

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

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