Question 4
Find all values of the real parameter $a$ for which the system
$$
\left\{
\begin{array}{c}
x^{2}+5x+y^{2}-y-|x-5y+5|=51 \\
a x - y - 5a + 2 = 0
\end{array}
\right.
$$
has exactly 2 distinct real solutions.
$$
\left\{
\begin{array}{c}
x^{2}+5x+y^{2}-y-|x-5y+5|=51 \\
a x - y - 5a + 2 = 0
\end{array}
\right.
$$
has exactly 2 distinct real solutions.