Question 30
Let $a$, $b$, and $c$ be real numbers. Consider the system of simultaneous equations in variables $x$ and $y$:
$$
\begin{aligned}
a x + b y &= c - 1 \\
(a + 5) x + (b + 3) y &= c + 1
\end{aligned}
$$
Determine the value(s) of $c$ in terms of $a$ such that the system always has a solution for any $a$ and $b$.
$$
\begin{aligned}
a x + b y &= c - 1 \\
(a + 5) x + (b + 3) y &= c + 1
\end{aligned}
$$
Determine the value(s) of $c$ in terms of $a$ such that the system always has a solution for any $a$ and $b$.