Question 866765
{{{1/x+1/y=1/2}}}

leads to

{{{(x+y)/(xy)=1/2}}}

but {{{x+y=9}}}

so 

{{{9/(xy)=1/2}}}

this means
{{{y=18/x}}}


which leads to

{{{x+18/x=9}}}
{{{x^2-9x+18=0}}}

so that {{{x=3}}} or  {{{x=6}}}

then we can see:

{ (3,6), (6,3) }