Solve the following system of equations:
; .

⇒
Putting 1/x = u and 1/y = v, we get
v + u = 2 … (i)
v - u = 6 … (ii)
Subtracting (i) and (ii),
2u = -4 or u = -2;
Hence x = - ½ .
Substituting u = -2 in (i),
v = 4.
Hence y = ¼ .
The solution set is {- ½ , ¼}.