$$3x+2y=6$$
$x=-\frac{2y}{3}+2$
$$3x=6-2y$$
$$\frac{3x}{3}=\frac{6-2y}{3}$$
$$x=\frac{6-2y}{3}$$
$$x=-\frac{2y}{3}+2$$
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$y=-\frac{3x}{2}+3$
$$2y=6-3x$$
$$\frac{2y}{2}=\frac{6-3x}{2}$$
$$y=\frac{6-3x}{2}$$
$$y=-\frac{3x}{2}+3$$