Understanding a proof that $17\mid (2x+3y)$ iff $17\mid(9x +5y)$ I was studying the number theory and came across this question. 
Example 1.1. Let $x$ and $y$ be integers. Prove that $2x + 3y$ is divisible by 17 if and only if $9x + 5y$ is divisible by 17.
Solution. $17 \mid (2x + 3y) \implies 17 | [13(2x + 3y)]$, or $17 \mid (26x + 39y) \implies 17 \mid (9x + 5y)$. Conversely, $17 \mid (9x + 5y) \implies 17 \mid [4(9x + 5y)]$, or $17 \mid (36x + 20y) \implies 17 \mid (2x + 3y)$.
I have a difficulty understanding how $$17\mid(26x+39y)$$ implies $$17\mid (9x+5y)$$ and vice versa. 
I know this question as already been asked here but I didn't understand from that answer and since I'm new to Math SE, I don't have enough points to add a comment to that post to clarify that answer.

Note that $26=17+9$ and $39=34+5$ 
Therefore working in mod (17) you can replace, $26$ with $9$ and $39$ with $5$ 
