Question

solve the following pair of linear equation by reducing them to a pair of linear equation 5/x+y +1/x-y = 2 10/x+y + 3/x-y =5

Answer 1

Refer to the attachment above....

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Answer 2

Given:

$\frac{5}{x+y}+\frac{1}{x-y}=2$

$\frac{10}{x+y}+\frac{3}{x-y}=5$

To find:

The solution of pair of linear equation.

Solution:

Let

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

Substitute the values

$5u+v=2$....(1)

$10u+3v=5$...(2)

Equation (1) multiply by 3 and then subtract equation (2) from equation (1)

$5u=1$

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

Substitute the value of u in equation (1)

$1+v=2$

$v=2-1=1$

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

$x+y=5$...(3)

$1=\frac{1}{x-y}$

$x-y=1$...(4)

Adding equation (3) and (4)

$2x=6$

$\implies x=\frac{6}{2}=3$

Substitute the value of x in equation (3)

$3+y=5$

$y=5-3=2$