Question 746083
{{{ 6x + 4y = 48 }}}
Divide both sides by {{{ 2 }}}
{{{ 3x + 2y = 24 }}}
{{{ 2y = -3x + 24 }}}
{{{ y = (-3/2)*x + 12 }}}
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{{{ x*y = x*( (-3/2)*x + 12 ) }}}
{{{ (-3/2)*x^2 + 12x }}}
This is a maximum at {{{ x = -b/(2a) }}}
{{{ x = -12/( 2*(-3/2)) }}}
{{{ x = 12 / 3 }}}
{{{ x = 4 }}}
When {{{ x = 4 }}}, 
{{{ y = (-3/2)*x + 12 }}}
{{{ y = (-3/2)*4 + 12 }}}
{{{ y = -6 + 12 }}}
{{{ y = 6 }}}
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The numbers are 4 and 6
check:
The 2 curves are
{{{ y = (-3/2)*x + 12 }}}
and
{{{ x*y = 4*6 }}}
{{{ y = 24/x }}}
Here's the 2 plots along with the parabola that tells you
the value of the product at the intersection.
{{{ graph( 400, 400, -10, 10, -4, 30, (-3/2)*x + 12, 24/x, (-3/2)*x^2 + 12x ) }}}