6/(x + y) 7/(x - y) = 3 and 1/2(x + y) = 1/3(x y)

Answer:
We have two linear equation As:

$\frac{6}{x+y} - \frac{7}{x-y} = 3$        And  $\frac{1}{2\left(x +y \right)} = \frac{1}{3 \left( x - y \right)}$

Let  $\frac{1}{x + y }$   = m      And  $\frac{1}{x - y}$  = n 

Then our equations are

6m -7n  = 3                             -------------- 1

$\frac{1}{2}$m  = $\frac{1}{3}$n

3m  = 2n                -------------------  2

SO 
m   = $\frac{2}{3}$n    in equation 1 we get
6( $\frac{2}{3}$n ) - 7n  = 3

4n - 7n  = 3
-3n = 3

n = -1 

Now put value of n = -1 in equation 2 we get

m = $-\frac{2}{3}$

But we assume $\frac{1}{x + y }$   = m     And  $\frac{1}{x - y}$  = n  So,
$\frac{1}{x + y }$  = $-\frac{2}{3}$

-2x -2y = 3

2 x + 2y = -3                            -------------------- 3

And 
$\frac{1}{x - y}$ = -1

- x + y = 1                             -----------------------  4

Now we multily in equation 4 and get

-2x +2y = 2                         ------------------------  5

Now add equation 3 and 5 we get

4y  = -1

y = $-\frac{1}{4}$

And ( ​equation 3 ) ​ - ( equation 5 )  we get

4x  = -5

x = $-\frac{5}{4}$


So x = $-\frac{5}{4}$    And  y = $-\frac{1}{4}$                            ( Ans )