Solve the system of equations: $$\begin{cases} 2x + 7(x+y) = 408 \\ 2y + 8(x+y) = 408 \end{cases}$$

To solve the system of equations, we will first simplify each equation:

$$\begin{cases} 2x + 7x + 7y = 408 \\ 2y + 8x + 8y = 408 \end{cases}$$

$$\begin{cases} 9x + 7y = 408 \\ 8x + 10y = 408 \end{cases}$$

Let's multiply the first equation by 10 and the second equation by 7 to eliminate the variable $$y$$:

$$\begin{cases} 90x + 70y = 4080 \\ 56x + 70y = 2856 \end{cases}$$

Subtract the second equation from the first:

$$(90x - 56x) + (70y - 70y) = 4080 - 2856$$
$$34x = 1224$$
$$x = \frac{1224}{34}$$
$$x = 36$$

Now, substitute the value of $$x$$ into the first original equation:

$$9(36) + 7y = 408$$
$$324 + 7y = 408$$
$$7y = 408 - 324$$
$$7y = 84$$
$$y = \frac{84}{7}$$
$$y = 12$$

So, the solution to the system of equations is $$x = 36$$ and $$y = 12$$.

Answer: x = 36, y = 12