Question 74
Anna, Anne and Anni seek for real solutions $(x, y)$ to the system of equations
$$
\begin{cases} 4x^3y - x^4 - 3x^2y^2 = 2021, \\ 4y^3x - y^4 - 3y^2x^2 = 2021. \end{cases}
$$
Anna claims that the system of equations has a solution. Anne claims that the system of equations has no solution but at least one of the two equations has solutions. Anni claims that the system of equations has no solution and, even worse, neither of the two equations alone has a solution. Who is right?
$$
\begin{cases} 4x^3y - x^4 - 3x^2y^2 = 2021, \\ 4y^3x - y^4 - 3y^2x^2 = 2021. \end{cases}
$$
Anna claims that the system of equations has a solution. Anne claims that the system of equations has no solution but at least one of the two equations has solutions. Anni claims that the system of equations has no solution and, even worse, neither of the two equations alone has a solution. Who is right?