$$6x-3y+1=0$$
$x=\frac{y}{2}-\frac{1}{6}$
$$6x+1=3y$$
$$6x=3y-1$$
$$\frac{6x}{6}=\frac{3y-1}{6}$$
$$x=\frac{3y-1}{6}$$
$$x=\frac{y}{2}-\frac{1}{6}$$
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$y=2x+\frac{1}{3}$
$$-3y+1=-6x$$
$$-3y=-6x-1$$
$$\frac{-3y}{-3}=\frac{-6x-1}{-3}$$
$$y=\frac{-6x-1}{-3}$$
$$y=2x+\frac{1}{3}$$
