Hello,

multiply the first one by 2 :

Add the two equations :

Complete the square :

Hence

Let's do the first case : (1)

Substitute in the equation :

So you have the system :

For the second case : (2)

Substitute in the very first equation :

So you have the system :

Also, be careful of the extraneous solutions.

Yah I know it's very long... I may have gone the wrong way ><

The first system gives awful solutions, but the second system gives nice solutions : (2,sqrt(2)) and (sqrt(2),2)