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Math Help - trouble understanding free varibles

  1. #1
    Junior Member
    Joined
    Feb 2009
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    49

    trouble understanding free varibles

    hey guys

    slighlty confused with understanding free variables

    for example
    x=y+z
    y=z

    woud z be the free variable? if so why???

    and heres an example i made up

    x=-2y+z
    y=z
    5x= w

    what are the free variables? z and w?? why?


    would this be a good stragety to follow

    say u have x=y+z
    y=z like in the first example....

    cross out all the variables which have an x and a y, since they are definined.. and the reamining none crossed out terms are the free variables ?

    thanks guys and gals
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  2. #2
    MHF Contributor

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    Quote Originally Posted by mpl06c View Post
    hey guys

    slighlty confused with understanding free variables

    for example
    x=y+z
    y=z

    woud z be the free variable? if so why???
    Yes, you are "free" to choose z to be anything you want, then you can calculate x and y from that. Note that being a "free variable"is not an "intrisic property" but depends on how the equations are written. Agebraically, x= y+ z, z= y is exactly the same but now the "free variable" is y. Of course, those systems could be written as x= 2z, y= z or x= 2y, z= y, making the "free variable" more evident.

    and heres an example i made up

    x=-2y+z
    y=z
    5x= w

    what are the free variables? z and w?? why?
    That's a bad example- you have three equations to determine the two variables x and y. Also, in order to talk about "free variables" all of your equations should just have "x= " or "y= ", etc., not "5x= ". Writing that last equation as x= w/5, we could have x= -2z+ z= -z, y= z and then, once x has been determined, w= 5x= -5z. The only "free variable" is z.


    would this be a good stragety to follow

    say u have x=y+z
    y=z like in the first example....

    cross out all the variables which have an x and a y, since they are definined.. and the reamining none crossed out terms are the free variables ?

    thanks guys and gals
    No. Write x= and y= with as few variables as possible on the right side, cancelling all you can. Then the variables left on the right are "free variables".
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