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