Question 433315

{{{x+y=15}}}

{{{1/x+1/y=3/10}}}
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{{{x+y=15}}}......solve for {{{x}}}
{{{x=15-y}}}.....plug in {{{1/x+1/y=3/10}}}

{{{1/(15-y)+1/y=3/10}}}

{{{(y+15-y)/y(15-y)=3/10}}}....cross multiply

{{{150=45y-3y^2}}}

{{{3y^2-45y+150=0}}}........solve quadratic


{{{y= (-(-45) +- sqrt((-45)^2-4*3*150 ))/(2*3) }}} 

{{{y= (45 +- sqrt(2025-1800 ))/6 }}}

{{{y= (45 +- sqrt(225))/6 }}}

{{{y= (45 +- 15)/6 }}}

{{{y1= (45 +15))/6 }}}


{{{y1= 60/6 }}}

{{{y1= 10 }}}


{{{y2= (45 -15))/6 }}}


{{{y2= 30/6 }}}

{{{y2= 5 }}}.....so  {{{y= 10 }}} or  {{{y= 5 }}}

now find {{{x}}}


{{{x+10=15}}}

{{{x=15-10}}}

{{{x=5}}}.....or


{{{x=15-5}}}

{{{x=10}}}

check:

{{{x=5}}} and {{{y=10}}}

{{{x+y=15}}}

{{{5+10=15}}}

{{{15=15}}}

their reciprocal:

{{{1/x+1/y=3/10}}}

{{{1/5+1/10=3/10}}}..common denominator

{{{(2+1)/10=3/10}}}

{{{3/10=3/10}}}

we will have same result if {{{x=10}}} and {{{y=5}}}