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Find values of K for which k has no solution, many solutions a unique solution

  1. Apr 8, 2010 #1
    1. The problem statement, all variables and given/known data

    Find values of K for which k has no solution, many solutions a unique solution

    2. Relevant equations

    x + ky = 1
    kx + y =1


    3. The attempt at a solution

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  3. Apr 8, 2010 #2

    LCKurtz

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    Gold Member

    What in the world is an expression like

    [tex]\frac{\binom{x+ky=1}{kx+y=1}}{y}[/tex]

    supposed to mean?

    Do you know Cramer's rule? Can you find a k that makes the equations dependent? Inconsistent?
     
  4. Apr 9, 2010 #3
    Method I: Try to solve the system for x and y as a function of k. Now check for which values of k the solution makes no sense (for example, if you have to divide by 0). Those are the values for which the system is inconsistent, so no solutions.

    Method II: graphical method. The two equations give two lines in the plane. If the cut at a point, the system is fine. If they're the same line, the system has many solutions. If they're parallel, the system has no solutions.
     
  5. Apr 9, 2010 #4

    Mark44

    Staff: Mentor

    The problem statement is shown as
    It makes more sense as "Find values of k for which the system of equations has no solution, many solutions, a unique solution."
     
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