I am currently studying for my upcoming algebra exam and I was wondering if anybody could explain to me this example of a very basic CRT question.
If $x=38$ then $x \equiv 2 \pmod{9}$ and $x \equiv 3 \pmod{7}$.
Solving this, I start by turning the first equation into $2+9y$ and then input it to $2+9y \equiv 3 \pmod 7$. However from here I don't understand why the example gives $2y \equiv 1 \pmod7 \rightarrow y \equiv 4 \pmod 7$ (I get how it went from that to $y \equiv 4 \pmod 7$).
I thought it would be $(2+9y-3)/7$ so $(9y-1)/7$ or is there a better way of getting the answer? Thanks!