Question

2/x+y + 3/x-y = 1
8/x+y - 7/x-y = 5/6

Find the value of x and y.
Actually, I am getting my answer wrong. So, please help me out

Answer 1

Answer:

x = 5,  y = -1

Step-by-step explanation:

Put A = 1/(x+y) and B = 1/(x-y).  Then the equations are:

      2A + 3B = 1      ... (1)

      8A - 7B = 5/6      ... (2)

Subtracting 4 times equation (1) from equation (2) gives

   -7B - 12B = 5/6 - 4   =>   -19B = -19/6   =>   B = 1/6   =>    1/(x-y) = 1/6

=> x-y = 6      ... (3)

Substituting B = 1/6 into equation (1) now gives

  2A + 1/2 = 1   =>   2A = 1/2   =>   A = 1/4   =>   1/(x+y) = 1/4

=>  x+y = 4      ... (4)

Adding equations (3) and (4) gives:

2x = 10  => x = 5

Substituting this into equation (4) gives:

y = 4-x = 4-5 = -1.