Question 48025
{{{ (x/a) + (y/b) = 1 }}}


(3,-2) --> {{{ (3/a) + ((-2)/b) = 1 }}}
--> now multiply all terms by ab
{{{ (3/a)(ab) + ((-2)/b)(ab) = (ab) }}}
{{{ 3b - 2a = ab }}}


(9,2) --> {{{ (9/a) + (2/b) = 1 }}}
--> now multiply all terms by ab, again
{{{ (9/a)(ab) + (2/b)(ab) = (ab) }}}
{{{ 9b + 2a = ab }}}


Now we have
3b - 2a = ab and
9b + 2a = ab


Lets add them:
12b = 2ab
2a = 12
--> a = 6


Now, {{{ 9b + 2a = ab }}} gives 9b + 12 = 6b
3b = -12
b = -4


So we have {{{ (x/6) + (y/(-4)) = 1 }}}
{{{ (x/6) - (y/4) = 1 }}}


CHECK: use (3,-2):
{{{ (3/6) - ((-2)/4) }}}
{{{ (1/2) + (1/2) }}}
is 1... correct


CHECK: use (9,2)
{{{ (9/6) - (2/4) }}}
{{{ (3/2) - (1/2) }}}
is 1... correct


jon