$$3y= \frac{ x }{ 2 } + \frac{ z }{ 3 }$$
$x=-\frac{2z}{3}+6y$
$$18y=3x+2z$$
$$3x+2z=18y$$
$$3x=18y-2z$$
$$\frac{3x}{3}=\frac{18y-2z}{3}$$
$$x=\frac{18y-2z}{3}$$
$$x=-\frac{2z}{3}+6y$$
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$y=\frac{x}{6}+\frac{z}{9}$
$$\frac{18y}{18}=\frac{3x+2z}{18}$$
$$y=\frac{3x+2z}{18}$$
$$y=\frac{x}{6}+\frac{z}{9}$$
