方程组 $\left\{\begin{array}{c}x+y=5\\ x-y=3\end{array}\right.$ 的解是 $($ 　　 $)$

A．

$\left\{\begin{array}{c}x=2\\ y=3\end{array}\right.$

B．

$\left\{\begin{array}{c}x=3\\ y=2\end{array}\right.$

C．

$\left\{\begin{array}{c}x=4\\ y=1\end{array}\right.$

D．

$\left\{\begin{array}{c}x=1\\ y=4\end{array}\right.$