Q&A #3962

Teachers' Lounge Discussion: Algebra

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From: Pat Ballew

To: Teacher2Teacher Public Discussion
Date: 2000122122:41:35
Subject: Re: Re: A special linear equation

I will proceed with your assumption that x>y>0 although I see no
reason to exclude the negatives in this problem (probably an oversight
on my part).... but 
Given that x+y = k(x-y) 
we proceed to x+y = kx-ky 

which leads to ky+y = kx-x

and (k+1)y= (k-1)x
to produce y= ------   x  

at this point we see that for every value of k, we can let x = k+1,
and y= k-1 and we get a solution.  Since this will work for all k>1
you have your infinite solution set. 

Hope I wrote that correctly...
Pat Ballew,
Misawa, Jp

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