Question

Solve the following systems of equations:
3/(x + y) + 2/(x – y) = 2
9/(x + y) – 4/(x – y) = 1

Answer 1

Solve the following systems of equations:

3/(x + y) + 2/(x – y) = 2

9/(x + y) – 4/(x – y) = 1

The values of x and y are:

x = 5/2

y = 1/2

Given,

3/(x + y) + 2/(x – y) = 2

9/(x + y) – 4/(x – y) = 1

Let 1/(x+y) = u and 1/(x-y) = v

Therefore, we have,

3u + 2v = 2    ..........(1)

9u – 4v = 1    ...........(2)

solving the above 2 equations  (1) and (2), we get,

u = 1/3

v = 1/2

Now, we have,

1/(x+y) = 1/3

⇒ x+y = 3  .........(3)

1/(x-y) = 1/2

⇒ x-y = 2  ..........(4)

solving the above 2 equations  (3) and (4), we get,

x = 5/2

y = 1/2