elementary number theory - Decrypting an Affine Cipher $e(m)=am+bpmod{27}$ knowing $e(8)equiv 14$ and $e(26)equiv 5$

I began by setting up a system of linear equations:
$$14\equiv 8a+b \pmod{27}$$
$$5\equiv 26a+b\pmod{27}$$
and then subtracted them to get: $9\equiv 9a \pmod{27}$. I know $9$ doesn't have a multiplicative inverse modulo $27$ but $a=1$ would solve this. I'm afraid I must be making some mistake somewhere, however, as solving this all the way through gives me $b=6$ and then translating the message doesn't quite make sense.

Answer

$$9a\equiv 9 \mod{27}$$
$$a \equiv1 \mod3$$

$$\therefore a=1+3k$$
$$b\equiv14-8a \mod{27}$$
$$b=14-8(1+3k)+27m$$
$$\therefore b=6-24k+27m$$
Where $k,m\in\mathbb{Z}$.