Answer
Not Conservative
Work Step by Step
For a vector field to be Conservative, $\dfrac{\partial f}{\partial y}=\dfrac{\partial g}{\partial x}$
We have: $f(x,y)=-y$ and $g(x,y)=x+y$
Thus, $\dfrac{\partial f}{\partial y}=-1$ and $\dfrac{\partial g}{\partial x}=1 $
So, $\dfrac{\partial f}{\partial y} \neq \dfrac{\partial g}{\partial x}$
Therefore, a vector field $F$ is Not Conservative.
