Prove that for all integers $a$, $b$ and $d$, if $d$ |$2a + b$ and $d$ | $3a + b$, then $d$ | $a$ and $d$ | $b$

Question

I'm having trouble proving this statement. I've assumed $d | 2a + b$ and $d | 3a + b$ and then isolated $a$ on both equations and $b$ on both equations and I can't get any of these 4 to look like $a=dm$ for int m nor any counter examples. Can anyone help me out?