$$4x+3=2y+5$$
$x=\frac{y+1}{2}$
$$4x=2y+5-3$$
$$4x=2y+2$$
$$\frac{4x}{4}=\frac{2y+2}{4}$$
$$x=\frac{2y+2}{4}$$
$$x=\frac{y+1}{2}$$
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$y=2x-1$
$$2y+5=4x+3$$
$$2y=4x+3-5$$
$$2y=4x-2$$
$$\frac{2y}{2}=\frac{4x-2}{2}$$
$$y=\frac{4x-2}{2}$$
$$y=2x-1$$