Deriving the Modigliani--Miller Theorem
The first equation can be written as:

$$ r_E(Levered) = \frac{E+D}{E}r_E(Unlevered) - \frac{D}{E}r_D $$

Then, isolating the unlevered return gives:

$$ r_E(Unlevered) = \frac{E}{E+D}r_E(Levered) + \frac{D}{E+D}r_D$$

And this is the WACC.