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