Question

4/x+y=2/x-y=5, 25 /x+y-3/x-y=1 solve with steps ​

Answer 1

Answer: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

Step-by-step explanation: