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