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