Question 917720
{{{system(2/x - 3/y = 2 , 4/x + 9/y + 1 = 0)}}}
With the "change of variable" {{{a=1/x}}} and {{{b=1/y}}} ,
the system of equations turns into
{{{system(2a-3b=2,4a+9b+1=0)}}}<-->{{{system(2a-3b=2,4a+9b=-1)}}} .
Multiplying the first equation times (-2) we get
{{{-4a+6b=-4}}} ,
and adding that to the second equation, we get
{{{15b=-5}}}-->{{{b=-5/15}}}-->{{{b=-1/3}}} .
Substituting that value into {{{2a-3b=2}}} we get
{{{2a-3(-1/3)=2}}}-->{{{2a+1=2}}}-->{{{2a=2-1}}}-->{{{2a=1}}}-->{{{a=1/2}}} .
going back to the original variables:
{{{1/x=1/2}}}-->{{{x=2}}}
{{{1/y=-1/3}}}-->{{{y=-3}}}