$$10b+a=10a+b-9$$
$a=b+1$
$$10b+a-10a=b-9$$
$$10b-9a=b-9$$
$$-9a=b-9-10b$$
$$-9a=-9b-9$$
$$\frac{-9a}{-9}=\frac{-9b-9}{-9}$$
$$a=\frac{-9b-9}{-9}$$
$$a=b+1$$
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$b=a-1$
$$10b+a-b=10a-9$$
$$9b+a=10a-9$$
$$9b=10a-9-a$$
$$9b=9a-9$$
$$\frac{9b}{9}=\frac{9a-9}{9}$$
$$b=\frac{9a-9}{9}$$
$$b=a-1$$
