5. (4 points) Let two sequences of numbers $\left(x_{0}, x_{1}, \ldots, x_{2009}\right)$, $\left(y_{0}, y_{1}, \ldots, y_{2009}\right)$ be constructed according to the following rules:
a) $x_{0}=12, x_{1}=\frac{1}{3}, y_{0}=4, y_{1}=\frac{1}{18}$,

b) $x_{i+1}=x_{i-1}+4 x_{i}$ and $y_{i+1}=y_{i-1}-4 y_{i}$ for $i=1, \ldots, 2008$.

Calculate the value of $x_{2009} y_{2008}+x_{2008} y_{2009}$.
5. 2 .

$+(4$ points) - solution is correct

+- (3 points) - the idea of the recurrence relation is proven, but there are arithmetic errors in the solution

-+ (2 points) - the idea of the recurrence relation is formulated, but the problem is not completed