Lecture 8, problem 8.16

I got 1 pair, but the answer says 2. 1/x+1/y=1/5.   5(x+y)=xy.  xy-5(x+y)+25=25. (x-5)(y-5)=25. 25=1*25=5*5=25*1=(-1)*(-25)=(-5)*(-5)=(-25)*(-1) This means that the solutions to the equation are (6,30), (10,10), (30, 6), (4, -20), (0, 0), (-20, 4), but 0<x<y, so the only solution is (6, 30). This means that the answer is 1.