4 x = 20 - 3 x + y = - 7 The solution to the

Choice C is correct. It's given that $4x=20$ and $-3x+y=-7$ is a system of equations with a solution $\left(x,y\right)$. Adding the second equation in the given system to the first equation yields $4x+(-3x+y)=20+\left(-7\right)$, which is equivalent to $x+y=13$. Thus, the value of $x+y$ is $13$. 

Choice A is incorrect. This represents the value of $-2\left(x+y\right)-1$.

Choice B is incorrect. This represents the value of $-\left(x+y\right)$.

Choice D is incorrect. This represents the value of $2\left(x+y\right)+1$.