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Algebra Difficulty 3.0 AMC 10/12 Find the answer Canada

Suppose that $a$ , $b$ and $c$ are three numbers with
$a + b = 3$
$ac + b = 18$
$bc + a = 6$
The value of $c$ is

(A) $2$ (B) $11$ (C) $3$ (D) $6$ (E) $7$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.