Teacher2Teacher 
Q&A #3962 
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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(xy) we proceed to x+y = kxky which leads to ky+y = kxx and (k+1)y= (k1)x k1 to produce y=  x (k+1) at this point we see that for every value of k, we can let x = k+1, and y= k1 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 Math Words, and other words of interest http://www.geocities.com/etyindex.html
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