#### Answer

$$-e^{-4}$$

#### Work Step by Step

Given $$\lim _{(x, y) \rightarrow(1,-3)}(2 x+y) e^{-x+y}$$
Since $ (2 x+y) e^{-x+y}$ is continuous, then
\begin{align*}
\lim _{(x, y) \rightarrow(1,-3)}(2 x+y) e^{-x+y}&=(2 \cdot 1-3) e^{-1-3}\\
&=-e^{-4}
\end{align*}