Question 670835
The equation of the line through
(a,0) and (0,b) has slope = {{{ b/a }}}
and the y-intercept is {{{ b }}}
The equation is {{{ y = (b/a)*x + b }}}
{{{ y = x }}}
{{{ x = (b/a)*x + b }}}
{{{ ( 1 - (b/a) )*x  = b }}}
{{{ ( ( a - b ) / a ) * x  = b }}}
{{{ x = ( a / ( a - b ) )*b }}}
{{{ x = ( a*b ) / ( a - b ) }}}
And, since {{{ y = x }}}, the intersection is at
( (a*b)/( a-b ) , (a*b)/( a-b ) ) answer
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check answer:
Suppose {{{ a = 3 }}} , {{{ b = 7 }}}
{{{ y = ( 7/3 )*x  + 7 }}}
{{{ y = x }}}
{{{ (7/3)*x - x = -7 }}}
{{{ (4/3)*x = -7 }}}
{{{ x = -21/4 }}}
and
{{{ x = ( a*b ) / ( a - b ) }}} 
{{{ x = 21 / ( 3 - 7 ) }}}
{{{ x = -21/4 }}}
{{{ y = -21/4 }}}
OK