Question 842617
8/x + 6/y = 6 and 1/x + 1/y = 1/6
8/x + 6/y = 6 and 1/x + 1/y = 1/6
multiply the second equation by 36
36( 1/x + 1/y = 1/6 ) = 36/x + 36/y = 6
Since 8/x + 6/y = 6
8/x + 6/y = 36/x + 36/y
add -8/x -6/y to each side
0 = 28/x + 30/y
add -30/y to each side
{{{-30/y = 28/x}}}
do cross products
28y = -30x
divide by 28
y = {{{(-30/28)*x}}}
substitute {{{(-30/28)*x}}} for y in 1/x + 1/y = 1/6
{{{1/x + 1/((-30/28)*x) = 1/6}}}
{{{1/x - 1/((30/28)*x) = 1/6}}}
{{{1/x - 28/(30*x) = 1/6}}}
{{{(30/30)*(1/x) - 28/(30*x) = 1/6}}}
{{{(30/(30*x)) - 28/(30*x) = 1/6}}}
{{{(2/(30*x))  = 1/6}}}
do cross products
30x=12
divide each side by 30
x = 12/30 = 2/5
We previously determined that y = {{{(-30/28)*x}}},
so substituting 2/5 for x we have
y = {{{(-30/28)*(2/5)}}}
y = {{{(-60/140)}}} = {{{-3/7}}}
summarizing x = 2/5 , y = -3/7