Question

solve 40/x+y + 2/x-y =2 ;25/x+y - 3/x-y =1

Answer 1

Answer:

I hope it will help you.

Answer 2

Answer:

$x = \frac{161}{8} \\ \\ y =\frac{9}{8}$

Step-by-step explanation:

To solve this

Let

$\frac{1}{x + y} = a \\ \\ \frac{1}{x - y} = b$

Substitute these values to the given equations

$40a + 2b = 2 \\ \\ or \\ \\ 20a + b = 1 \: \: \: ...eq1 \\ \\ 25a - 3b = 1 \: \: \: eq2$

multiply equation 1 by 3 and subtract both equations

$60a + 3b = 3 \\ 25a - 3b = 1 \\ - - - - - - \\ 85a = 4 \\ \\ a = \frac{4}{85} \\ \\ 20 \times \frac{4}{85} + b = 1 \\ \\ b = 1 - \frac{80}{85} \\ \\ b = \frac{5}{85} = \frac{1}{19}$

put these values to

$\frac{1}{x + y} = \frac{4}{85} \\ \\ \frac{1}{x - y} = \frac{1}{19} \\ \\ 4x + 4y = 85 \\ 4x - 4y = 76 \\ \\ solve \: these \: two \: \\ 8x = 161 \\ \\ x = \frac{161}{8} \\ \\ y =\frac{9}{8}$

Hope it helps you