discrete mathematics and proofs Let $a$ and $b$ be in the universe of all integers, so that $2a + 3b$ is a multiple of $17$.
Prove that $17$ divides $9a + 5b$. 
In my textbook they do $17|(2a+3b) \implies 17|(-4)(2a+3b)$.
They do this with the theorem of $a|b \implies a|bx$.
However, I don't know how the book got $x=-4$.
What is the math behind this?
This is just a section of the steps that complete the proof.
Once I know how the book figured out $x$ was $-4$ then i will be happy.

*

*$9a+5b-x(2a+3b)=17a+17b$

*$(9-2x)a+(5-3x)b=17a+17b$

*$9-2x=17 \implies x=-4$

*$5-3x=17 \implies x=-4$
