Writing direct proofs Let $x$, $y$ be elements of $\mathbb{Z}$. Prove if $17\mid(2x+3y)$ then $17\mid(9x+5y)$.  Can someone give advice as to what method of proof should I use for this implication? Or simply what steps to take?

$\rm\begin{eqnarray}{\bf Hint}\ \ \  a\ (cx\!+\!dy)\!\!\!\!\!\!&\ - &\rm\! c\ (ax\!+\!by)\ \ =\ \ (ad\!-\!bc)y \\
\rm thus\ \ \ \  p\mid cx\!+\!dy \!\!\!\!&\iff&\rm\!\!\! p\mid ax\!+\!by\ \ if\ \ p\mid ad\!-\!bc,\,\ p\nmid a,c,\,\ p\ prime \end{eqnarray}$
