Equation (2) is incorrect. As you have a term which is not present in the original equation.
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?