Question

Solve the following pairs of equation by reducing them to a pair of linear equations.
$\frac{10}{x+y}+\frac{2}{x-y}=\mathrm{4...}\left(i\right)\frac{15}{x+y}-\frac{5}{x-y}=-\mathrm{2...}\left(ii\right)$

Answer 1

$\frac{10}{x+y}+\frac{2}{x-y}=\mathrm{4...}\left(i\right)\frac{15}{x+y}-\frac{5}{x-y}=-\mathrm{2...}\left(ii\right)Take\frac{1}{x+y}=u,\frac{1}{x-y}=v10u+2u=4\times 3...\left(iii\right)15u-5u=-2\times \mathrm{2...}\left(iv\right)30u+6u=1230u-10u=-4-++$
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$16u=164=110u+2\times 4=410u+2=4(since4=1)10u=2$
$4=\frac{1}{5}$
$\frac{1}{x+y}=\frac{1}{5}$
$5=x+y...\left(v\right)$
$\frac{1}{x+y}=1$
$1=x-y...\left(vi\right)$
From (v) and (vi)
$x+y=5$
$x-y=1$
___________
$2x=6$
$x=3$
$y=2$