Find all the solutions of each of the linear congruences below:

\begin{align}
&(a) &10x &\equiv 5 \pmod{15},\\
&(b) &6x &\equiv 7 \pmod{26},\\
&(c) &7x &\equiv 8 \pmod{11}.
\end{align}

I'm not entirely sure how to get these solutions by hand. I know how to prove there are solutions.

For example:

$(a) \quad\gcd(10,15)=5 $ and we know $5|5$.

From there I set $10x+15y=5$ and divide through by $5$. Leaving us with $2x+3y=1$. I know some solutions for $x$ and $y$, such as $x=-1$ and $y=1$, but that's all I have thus far.