Choice $D$ is correct. It's given by the first equation in the given system of equations that $x=10$. Substituting $10$ for $x$ in the second equation in the given system yields $y=10+21$, or $y=31$. Therefore, the value of $y$ is $31$.

Choice $A$ is incorrect and may result from conceptual or calculation errors.

Choice $B$ is incorrect. This is the value of $z$, not the value of $y$.

Choice $C$ is incorrect and may result from conceptual or calculation errors.