Find all solutions to this system of equations

(i)

(ii)

I take

3(ii) – 2(i) = 0

=> (2)

=> (3)

Therefor, I have these points.

(0,0)

(±√3, 0)

But x=±1 is also a solution. But that doesn't satisfy the right hand side in (3). I could have seen x=±1 and put it in (i) and (ii). But I didn't see that. Do I have a bad, nonsystematic method for solving this system of equation? How do I do it better?