Item 2.
Pick the smaller of \(a\) and \(b\) (here, assume it is \(b\)), and convert to a congruence modulo \(b\text{:}\)
\begin{equation*}
ax + by \equiv c \pmod{b}\text{.}
\end{equation*}
This will reduce to a congruence with one variable, \(x\text{:}\)
\begin{equation*}
ax \equiv c \pmod{b}\text{.}
\end{equation*}