Question 662458

{{{x+y= 18}}}.....1

{{{x*y=  56}}}......2
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{{{x+y= 18}}}.....1..solve for {{{x}}}

{{{x= 18-y}}}.....plug it in 2


{{{x*y=  56}}}......2

{{{(18-y)*y=  56}}}

{{{18y-y^2=  56}}}

{{{y^2-18y+56=0}}}...use quadratic formula to fin {{{y}}}


 {{{y = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} ...note that {{{a=1}}}, {{{b=-18}}} and {{{c=56}}}


{{{y = (-(-18) +- sqrt( (-18)^2-4*1*56 ))/(2*1) }}}


{{{y = (18 +- sqrt( 324-224 ))/2 }}}


{{{y = (18 +- sqrt( 100 ))/2 }}}

{{{y = (18 +- 10)/2 }}}


solutions:


{{{y = (18 + 10)/2 }}}

{{{y = 28/2 }}}

{{{highlight(y = 14) }}}


or


{{{y = (18 - 10)/2 }}}

{{{y = 8/2 }}}

{{{highlight(y = 4) }}}



now find {{{x}}}


{{{x= 18-y}}}...plug in {{{highlight(y = 14) }}}

{{{x= 18-14}}}

{{{highlight(x= 4)}}}


or


{{{x= 18-y}}}...plug in {{{highlight(y = 4) }}}

{{{x= 18-4}}}

{{{highlight(x= 14)}}}



you have two sets of solutions:


1. {{{highlight(x= 4)}}} and {{{highlight(y = 14) }}}

or

2.{{{highlight(x= 14)}}} and {{{highlight(y = 4) }}}