$$6x-2y=-18$$
$x=\frac{y-9}{3}$
$$6x=-18+2y$$
$$6x=2y-18$$
$$\frac{6x}{6}=\frac{2y-18}{6}$$
$$x=\frac{2y-18}{6}$$
$$x=\frac{y}{3}-3$$
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$y=3\left(x+3\right)$
$$-2y=-18-6x$$
$$-2y=-6x-18$$
$$\frac{-2y}{-2}=\frac{-6x-18}{-2}$$
$$y=\frac{-6x-18}{-2}$$
$$y=3x+9$$