Ahh! - Looking at your code more closely, I think I see the problem...
I think your first "plot" statement uses uses symbol1 (since you don't specify which symbol statement), and in your second plot statement "plot2" you specify y*x=1 (therefore it uses symbol1. Since symbol1 says to do a pointlabel, and since both plot and plot2 use symbol1, you get 2 pointlabels.
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