Question 1006945
{{{ x^2 + y^2 = 49}}} ..........eq.1 
{{{x+y=5 }}}.........eq.2
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{{{x+y=5 }}}.........eq.2.........solve for {{{x}}}

{{{x=5-y }}}.....substitute in eq.1


{{{ (5-y)^2 + y^2 = 49}}} ..........eq.1 ..solve for {{{y}}}

{{{ 25-10y+y^2 + y^2 = 49}}}

{{{ 2y^2-10y = 49-25}}}

{{{ 2y^2-10y = 24}}}......both sides divide by {{{2}}}

{{{ y^2-5y = 12}}}

{{{ y^2-5y -12=0}}}...use quadratic formula


{{{y = (-(-5) +- sqrt( (-5)^2-4*1*(-12) ))/(2*1) }}}


{{{y = (5 +- sqrt( 25+48 ))/2 }}}

{{{y = (5 +- sqrt( 73 ))/2 }}}

exact solutions:

{{{y = 5/2 + sqrt( 73 )/2 }}}
or
{{{y = 5/2 - sqrt( 73 )/2 }}}

now find {{{x}}}

{{{x=5-y }}}

{{{x=5-(5/2 + sqrt( 73 )/2) }}} 

{{{x=10-5/2-sqrt( 73 )/2) }}} 

{{{x=5/2-sqrt( 73 )/2) }}} 

or


{{{x=5-(5/2 - sqrt( 73 )/2) }}} 

{{{x=10/2-5/2+sqrt( 73 )/2) }}} 

{{{x=5/2+sqrt( 73 )/2) }}} 


so, exact solutions:

{{{x=5/2-sqrt( 73 )/2) }}}, {{{y = 5/2 + sqrt( 73 )/2 }}}
or
{{{x=5/2+sqrt( 73 )/2) }}}, {{{y = 5/2 - sqrt( 73 )/2 }}}