Question 1132110

{{{2/x+5/y=5/6 }}}........1)
{{{x/2+y/5=5 }}}........2)
----------------------------------------------

{{{2/x+5/y=5/6 }}}........1).....both sides multiply by {{{6xy}}}

{{{(6xy*2)/x+(6xy*5)/y=(6xy*5)/6 }}}

{{{12y+30x=5xy }}}........solve for {{{y}}}

{{{12y-5xy=-30x }}}

{{{(12-5x)y=-30x }}}

{{{y=-30x/(12-5x) }}}........1a)


{{{x/2+y/5=5 }}}........2)......both sides multiply by {{{10}}}

{{{10x/2+10y/5=10*5 }}}

{{{5x+2y=50 }}}........solve for {{{y}}}

{{{y=50/2-5x/2 }}}

{{{y=25-(5/2 )x}}}.....2a)


from  1a) and 2a) we have

{{{-30x/(12-5x) =25-(5/2 )x}}}.......solve for {{{x}}}

{{{5x/2 -30x/(12-5x) =25}}}

{{{(5x(12-5x))/2(12-5x) -(2*30x)/2(12-5x) =25}}}

{{{(60x-25x^2 -60x)/2(12-5x) =25}}}

{{{-25x^2 =25*2(12-5x)}}}..........simplify

{{{-x^2 =2(12-5x)}}}

{{{-x^2 =24-10x}}}

{{{0 =x^2-10x+24}}}....factor

{{{(x - 4) (x - 6)=0}}}
=> {{{x=4}}} or {{{x=6}}}

go to {{{y=25-(5/2 )x}}}.....2a), substitute {{{x}}}

{{{y=25-(5/2 )4}}}
{{{y=25-5*2 }}}
{{{y=25-10 }}}
{{{y=15 }}}

{{{y=25-(5/2 )6}}}
{{{y=25-5*3 }}}
{{{y=25-15 }}}
{{{y=10 }}}


solutions:

{{{x=4}}},{{{y=15 }}}
 
or 
{{{x=6}}},{{{y=10 }}}