Solve the equations.

Question

Solve for real numbers $x$ & $y$ : $$xy^2=15x^2+17xy+15y^2$$ $$x^2y=20x^2+3y^2$$.

It is my problem. Please help me

Answer 1

Hint: $x=0 \implies y=0\,$, otherwise let $y = tx$ and eliminate $x$ between:

$$ \require{cancel} \begin{cases} \begin{align} x^\bcancel{3} t^2 &= 15\cancel{x^2}+17\cancel{x^2} t+15\cancel{x^2} t^2 \\ x^\bcancel{3} t &= 20\cancel{x^2} + 3\cancel{x^2}t^2 \end{align} \end{cases} $$