$$\frac{2x}{3}+\frac{y}{2}=\frac{-7}{9}$$
$x=-\frac{3y}{4}-\frac{7}{6}$
$$6\times 2x+9y=2\left(-7\right)$$
$$12x+9y=2\left(-7\right)$$
$$12x+9y=-14$$
$$12x=-14-9y$$
$$12x=-9y-14$$
$$\frac{12x}{12}=\frac{-9y-14}{12}$$
$$x=\frac{-9y-14}{12}$$
$$x=-\frac{3y}{4}-\frac{7}{6}$$
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$y=-\frac{4x}{3}-\frac{14}{9}$
$$9y=-14-12x$$
$$9y=-12x-14$$
$$\frac{9y}{9}=\frac{-12x-14}{9}$$
$$y=\frac{-12x-14}{9}$$
$$y=-\frac{4x}{3}-\frac{14}{9}$$
