System of congruence equations I have a system of congruence eqs
$$
\begin{cases}
x \equiv 14 \pmod{98} \\
x \equiv 1 \pmod{28}
\end{cases}
$$
I have calculated $\text{gcd}(98,28) = 14$.
I can from the congruence eqs get $x = 14+98k$ and $x = 1+28m$.
I equate these
$$
14+98k = 1+28m \Leftrightarrow 28m - 98k = 13
$$
I know that $\text{gcd}(98,28) = 14$ is not divisible by 13 and therefore the system has no solutions.. Is this correct?

we get by definition $$x=14+98k_1$$ and $$x=1+28k_2$$ with $k_1,k_2$ are integers, thus we get
$$98k_1-28k_2=-13$$
this equation has no solutions, why?
