Question

solve for x and y
5/x+y 1/x-y =2 , 15/x+y - 5/x-y =-2
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Answer 1

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

$\frac{15}{x + y} - \frac{5}{x - y}$ = -2 --------> 2

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

⇒ 5u + v = 2------> 3

v = 2 - 5u

⇒ 15u - 5v = -2 --------> 4

Putting eq. 3 in eq. 4

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

15u - 10 + 25u = -2

40u = -2 + 10

40u = 8

u = $\frac{8}{40}$

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

Putting value of u in eq. 3

5 ( $\frac{1}{5}$ ) + v = 2

1 + v = 2

v = 2 - 1

$\fbox v = 1$

⇒ $\frac{1}{x + y} = u$

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

⇒ x + y = 5

x = 5 - y ------ > 5

⇒$\frac{1}{x - y} = v$

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

⇒ x - y = 1

Putting the value of x from eq.5

5 - y - y = 1

5 - 2y = 1

- 2y = 1 - 5

- 2y = - 4

$y = \frac{- 4}{- 2}$

$\fbox y=2$

Putting this value in eq 5

x = 5 - 2

$\fbox x=3$

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Answer 2

Answer:

hope it's correct mate