Question

Solve for x and y: `3/(x+y) + 2/(x−y) = 2, 9/(x+y) – 4/(x−y) = 1`

Answer 1

The given system of equations is

`3/(x+y) + 2/(x−y) = 2`               ………..(i)
`9/(x+y) – 4/(x−y) = 1  `              ………..(ii)
Substituting `1/(x+y) = u and 1/(x−y) = v`  in (i) and (ii), the given equations are changed to
3u + 2v = 2                          ………(iii)
9u – 4v = 1                           ………(iv)
Multiplying (i) by 2 and adding it with (ii), we get
15u = 4 + 1 ⇒ u = `1/3`
Multiplying (i) by 3 and subtracting (ii) from it, we get
6u + 4v = 6 – 1 ⇒ u = `5/10 = 1/2`
Therefore
x + y = 3                        ………….(v)
x – y = 2                         …………(vi)
Now, adding (v) and (vi) we have
2x = 5 ⇒ x = `5/2`
Substituting x = `5/2` in (v), we have
`5/2 + y = 3 ⇒ y = 3 – 5/2 = 1/2`
Hence,    ` x = 5/2 and y = 1/2`.