Question

solve x & y 5/x+y + 1/x-y =2 , 15/x+y - 5/x - y = -2​

Answer 1

Question:

Solve x and y

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

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

Solution:

Let $\dfrac{1}{x+y} = p$ and $\dfrac{1}{x-y} = q$

So,

5p + q = 2 (Equation 1)

15p - 5q = -2 (Equation 2)

Multiplying Equation 1 from 3

15p + 3q = 6 (Equation 3)

Subtracting Equation 2 from Equation 3

15p + 3q - 15p + 5q = 6 - (-2)

8q = 8

q = 1

Putting value in Equation 1

5p + q = 2

5p + 1 = 2

5p = 2 - 1

p = $\dfrac{1}{5}$

Putting values of p and q

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

x + y = 5 (Equation 4)

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

x - y = 1 (Equation 5)

Adding Equation 4 and Equation 5

x + y + x - y = 5 + 1

2x = 6

x = 3

Putting value in Equation 4

x + y = 5

3 + y = 5

y = 5 - 3 = 2

Hence,

x = 3

y = 2