$$2y-3x+4=0$$
$x=\frac{2\left(y+2\right)}{3}$
$$-3x+4=-2y$$
$$-3x=-2y-4$$
$$\frac{-3x}{-3}=\frac{-2y-4}{-3}$$
$$x=\frac{-2y-4}{-3}$$
$$x=\frac{2y+4}{3}$$
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$y=\frac{3x}{2}-2$
$$2y+4=3x$$
$$2y=3x-4$$
$$\frac{2y}{2}=\frac{3x-4}{2}$$
$$y=\frac{3x-4}{2}$$
$$y=\frac{3x}{2}-2$$
