$$2x+2y=2$$
$x=1-y$
$$2x=2-2y$$
$$\frac{2x}{2}=\frac{2-2y}{2}$$
$$x=\frac{2-2y}{2}$$
$$x=1-y$$
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$y=1-x$
$$2y=2-2x$$
$$\frac{2y}{2}=\frac{2-2x}{2}$$
$$y=\frac{2-2x}{2}$$
$$y=1-x$$