<PRE><B>Question 177697</B>
 {{{1/x}}} + {{{2/y}}} = 9
{{{7/x}}} + {{{11/y}}} = 54
:
multiply both equations by xy, results:
y +   2x = 9xy
7y + 11x = 54xy
:
multiply the 1st equation by 7, subtract the 2nd equation from it
7y + 14x = 63xy
7y + 11x = 54xy
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0 + 3x = 9xy
Divide both sides by 3x:
1 = 3y
y = {{{1/3}}}
:
find x
y +   2x = 9xy
{{{1/3}}} + 2x = {{{1/3}}}*9x
{{{1/3}}} + 2x = 3x
{{{1/3}}} = 3x - 2x
x = {{{1/3}}}
:
:
check solution
{{{7/x}}} + {{{11/y}}} = 54
substitute 1/3 for x and y
(3*7) + (3*11) = 54

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