The complex numbers $a$ and $b$ satisfy
\[a + \overline{b} = 2 - 7i.\]Find $\overline{a} + b.$
I recall that the conjugate of a complex number $x + yi$ is $\overline{x + yi} = x - yi.$ So, if I take the conjugate of both sides of the given equation, I get
\[\overline{a + \overline{b}} = \overline{2 - 7i}.\] Applying the properties of conjugates, I can write this as
\[\overline{a} + b = 2 + 7i.\]

