$$5 x - 3 y = 8$$
$x=\frac{3y+8}{5}$
$$5x=8+3y$$
$$5x=3y+8$$
$$\frac{5x}{5}=\frac{3y+8}{5}$$
$$x=\frac{3y+8}{5}$$
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$y=\frac{5x-8}{3}$
$$-3y=8-5x$$
$$\frac{-3y}{-3}=\frac{8-5x}{-3}$$
$$y=\frac{8-5x}{-3}$$
$$y=\frac{5x-8}{3}$$
