Question 62
Find all real values of $a$ such that the system
$$
\left\lvert\,
\begin{aligned}
& \frac{a x+y}{y+1}+\frac{a y+x}{x+1}=a \\
& a x^{2}+a y^{2}=(a-2) x y-x
\end{aligned}
\right.
$$
has a unique solution.
$$
\left\lvert\,
\begin{aligned}
& \frac{a x+y}{y+1}+\frac{a y+x}{x+1}=a \\
& a x^{2}+a y^{2}=(a-2) x y-x
\end{aligned}
\right.
$$
has a unique solution.