Question 845960
{{{2x+3y=6xy}}}
{{{ x-y=xy}}}
From eq. 2,
{{{x-y=xy}}}
{{{x=xy+y}}}
{{{x=y(x+1)}}}
{{{y=x/(x+1)}}}
Substitute into eq. 1,
{{{2x+3x/(x+1)=6x(x/(x+1))}}}
{{{2x(x+1)+3x=6x^2}}}
{{{2x^2+2x+3x=6x^2}}}
{{{4x^2-5x=0}}}
{{{x(4x-5)=0}}}
Two solutions:
{{{x=0}}}
Then
{{{y=0/(0+1)=0}}}
and
{{{4x-5=0}}}
{{{4x=5}}}
{{{x=5/4}}}
and 
{{{y=(5/4)/(5/4+1)=(5/4)/(9/4)=5/9}}}