jmc

We can begin by multiplying the second equation by two, giving us the following system of equations $$\begin{array}{rl}4u-5v& =23\\ 4u+8v& =-16\end{array}$$From here we simply subtract the second equation from the first. This gives us $(4u-5v)-(4u+8v)=23-(-16)$, which simplifies to $-13v=39$ or $v=-3$. We now know the value of $v$, so we can just plug this into the first equation in order to solve for $u$. This gives us $4u-5(-3)=23$, or $4u=8$ and $u=2$. Since $v=-3$ and $u=2$, $u+v=2+(-3)=\boxed{-1}$.