$$2 a = 3 b$$
$a=\frac{3b}{2}$
$$2a=3b$$
$$\frac{2a}{2}=\frac{3b}{2}$$
$$a=\frac{3b}{2}$$
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$b=\frac{2a}{3}$
$$3b=2a$$
$$\frac{3b}{3}=\frac{2a}{3}$$
$$b=\frac{2a}{3}$$