Track / Stage 5 / 36 of 400 #636 of 2000

$\therefore$ (10 points) Given $a, b$ are integers, and $a+9b$ is divisible by 5, prove that $8a+7b$ is also divisible by 5.

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

I solved it I didn't Skip

Official solution

Six, prompt:
$$8 a+7 b=8(a+9 b)-65 b .$$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.