Given the curve
$$K = \left\{ \begin{pmatrix} x \\ y \end{pmatrix} \in \mathbb{R}^2: x^2y^3+x^3y = 2\right\} $$
How can one prove that $K$ goes through the point $(1,1)$, is locally solvable by $y$ there and that the solution is monotonically decreasing?
This is what the grapher shows, but I don't know what to do to prove the above.
