System of linear equations

Discussion in 'Math' started by sadaf, Aug 8, 2010.

  1. sadaf

    Thread Starter New Member

    Aug 4, 2010
    25
    0
    Below there are two equations;

    1. 2x+3y=4
    2. 4x+6y=8

    can these equations have any solution?
    if it is then what is the solution and what is the common point where they meet?
    please tell me i am so confused...
     
  2. debjit625

    Well-Known Member

    Apr 17, 2010
    790
    186
    No,this cant have any solution
    Now using determinants we could determine if it could have any solution its like this
    Example
    ax + by = c
    dx + ey = f
    if (a*e) - (d*b) != 0 i.e.. not equal to zero then the system of linear equation have a unique solution.
    In your case
    (2*6) - (4*3) = 0 so it will not give you a unique solution

    Good luck
     
  3. Papabravo

    Expert

    Feb 24, 2006
    10,180
    1,800
    The other way to see this is to recognize that both equations are essentially the same. If you multiply both sides of the first equation by 2 you get the second equation. Hence the equations are not independent and therefore have no unique solution. Both equations represent the same line and so they have an infinite number of points in common.
     
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