Congruence system with same modulus and same variable? I have this particular problem:
$$\begin{cases}
3k \equiv 2 \pmod 8 \dots(*) \\
7k \equiv 2 \pmod 8 \dots(**)
\end{cases}
$$
I know that the solution for this is $k = 8q + 6$. I can find this easily if I solve one of the equations alone.
Now, let's assume I subtract $(*)$ from $(**)$. I get $4k\equiv0[8]$ and $k = 2q$, which isn't coherent.
For example, if I take $q = 2$ then $3k=12$, which does not satisfy $(*)$ (nor $(**)$).
I can't figure out where I messed up. Please help me to understand this.

Hint:
Multiply each congruence by the inverse mod. $8$ of the coefficient of $k$, and check if the answers are compatible.
