Question

Solve the following systems of equations:

`1/(2x) + 1/(3y) = 2`

`1/(3x) + 1/(2y) = 13/6`

Answer 1

Let `1/x = u` and `1/y = v` the given equations become

`u/2 + v/3 = 2`

`=> (3u + 2v)/6 = 2`

=> 3u + 2v = 12 .....(i)

And `u/3 + v/2 = 13/6`

`=> (2u + 3v)/6 = 13/6`

`=> v = 6/2 = 3`

Hence  `x = 1/u = 1/2`  and `y = 1/v = 1/3`

So, the solution of the given system o equation is `x = 1/2, y = 1/3`