# Thread: trouble understanding free varibles

1. ## 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

2. Originally Posted by mpl06c
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".