How to solve a congruence system? Here is a tricky congruence system to solve, I have tried to use the Chinese Remainder Theorem without success so far.
$$2x \equiv3\;(mod\;7)\\
x\equiv8\;(mod\;15)$$
Thank you very much
Li

\begin{split}
X&=15L+8\\
2X&=30L+16=30(7m+u)+16 
\end{split}
[ where $u$ can be $0,1,2,3,4,5,6$]
$$
2X=(210m+28u+14)+(2u+2)
$$
So $2u+2$ must leave remainder $3$ when divided by $7$,thus
\begin{split}
u&=4\\
2X&=210m+136.
\end{split}
Therefore $X=105m+68$.
