Question 1153062
{{{xy=30}}}...eq.1
{{{3x+y=1}}}...eq.2
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{{{xy=30}}}...eq.1, solve for {{{y}}}

{{{y=30/x}}}.........eq.1a

substitute in eq.2

{{{3x+30/x=1}}}...eq.2

{{{3x^2+30=x}}}

{{{3x^2-x+30=0}}}


 {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


 {{{x = (-(-1) +- sqrt( (-1)^2-4*3*30 ))/(2*3) }}}

 {{{x = (1 +- sqrt(1-360 ))/6 }}}

 {{{x = (1 +- i*sqrt(359 ))/6 }}}




solutions:

{{{x = (1 + i*sqrt(359 ))/6 }}} or {{{x = (1 - i*sqrt(359 ))/6 }}}


go to

{{{y=30/x}}}.........eq.1a, substitute {{{x}}}


{{{y=30/(1 + i*sqrt(359 ))/6 }}}

{{{y=180/(1 + i*sqrt(359 )) }}}

{{{x = (1 +- i*sqrt(359 ))/6 }}}
or

{{{y=30/(1 - i*sqrt(359 ))/6 }}}

{{{y=180/(1 - i*sqrt(359 )) }}}