Question

Solve the following pair of linear equations: $\frac{10}{x+y}+\frac{2}{x-y}=4;\frac{15}{x+y}-\frac{5}{x-y}=-2$

Answer 1

Let $\frac{1}{x+y}=u\&\frac{1}{x-y}=v$

then

$(10u+2v=4)3$

$(15u-5v=-2)2$

$10u+2=4$

$u=\frac{1}{5}$

$-(30u-10v=-4)$

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$16v=16$

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$v=1;u=\frac{1}{5}=0.2$

$\frac{1}{x+y}=\frac{1}{5};x+y=5$
$\frac{1}{x-y}=1;x-y=1$

$x+y=5$

$x-y=1$

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$2x=6$

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$x=3\&y=2$