Question

2/x+y + 5/x-y = 3
7/x+y - 2/x-y = 4

Answer 1

Answer:

x = 9/4 and y = -3/4

Step-by-step explanation:

$\frac{2}{x + y} + \frac{5}{x - y} = 3 \\ \\ \frac{7}{x + y} - \frac{2}{x - y} = 4 \\ \\ taking \\ \: \frac{1}{x + y} = u \: \: \\ and \: \\ \frac{1}{x - y} = v \: \\ we \: have \: \\ 2u + 5v = 3 \\ \implies2u = 3 - 5v \\ \implies \: u = \frac{3 - 5v}{2} - - - (1) \\ again \\ 7u - 2v = 4 - - - (2)\\ \implies7( \frac{3 - 5v}{2} ) - 2v = 4 \\ \implies \frac{21 - 35v - 4v}{2} = 4 \\ \implies - 39v = - 21 + 8\\ \implies - 39v = - 13 \\ \implies \: v = \frac{1}{3} \\ using \: the \: value \: of \: v \: in \: (1) \\ u = \frac{3 - 5( \frac{1}{3} )}{2} \\ \implies u = \frac{ \frac{9 - 5}{3} }{2} \\ \implies \: u = \frac{4}{3 \times 2} \\ \implies \: u \: = \frac{2}{3}$

Now we have

$u = \frac{1}{x + y} \\ \implies \frac{2}{3} = \frac{1}{x + y} \\ \implies \: x + y = \frac{3}{2} - - - (3)\\ and \: \\ \implies \: v = \frac{1}{3} \\ \implies \frac{1}{x - y } = \frac{1}{3} \\ \implies \: x - y = 3 - - - (4)\\ \\ (3) + (4) \\ \implies2x = \frac{3 + 6}{2} \\ \implies \: x = \frac{9}{4} \\ and \\ \implies y = \frac{3}{2} - \frac{9}{4} \\ \implies \: y = \frac{6 - 9}{4} \\ \implies \: y = \frac{ - 3}{4}$