Question

5/x+y-2/x-y = -1 and 15/x+y+7/x-y=10 where x≠0,y≠0
​

Answer 1

Answer:

x = 3, y = 2

Step-by-step explanation:

$\frac{5}{x + y} - \frac{2}{x - y} = - 1 \: \: \: \: \frac{15}{x + y} + \frac{7}{x - y} = 10 \\ let \: \frac{1}{x + y} = a \: \: and \: \frac{1}{x - y} = b \\ 5a - 2b = - 1 \: \: \: equ \: (1) \\ 15a + 7b = 10 \: \: equ \: (2) \\ multiply \: equ \: (1) \: with \: 3 \\ 15a - 6b = - 3 \: \: \: equ \: (3) \\ subtracting \: (3) - (2) \\ we \: get \\ b = 1 \\ substituting \: b \: in \: equ \: (1) \\ 5a - 2(1) = - 1 \\ 5a = - 1 + 2 = 1 \\ a = \frac{1}{5}$

$a = \frac{1}{x + y} = \frac{1}{5} \\ x + y = 5 \: \: equ \: (4)\\ b = \frac{1}{x - y} = 1 \\ x - y = 1 \: \: \: equ \: (5) \\ add \: equ \: (4) + (5) \\ we \: get \: \\ 2x = 6 \\ x = 3 \\ substitute \: x \: in \: equ \: (4) \\ 3 + y = 5 \\ y = 5 - 3 = 2 \\ y = 2$

hope you get your answer