《孙子算经》中记载了这样一道题：＂用一根绳子去量一根长木，绳子还剩余 4.5 尺；将绳子对折再量长木，长木还剩余 1 尺，木长多少尺？＂若设绳子长 x 尺，木长 y 尺．根据题意，可得列方程组
A. $\left\{\begin{array}{c}x+y=1 \\ x-\frac{1}{2} y=4.5\end{array}\right.$
B. $\left\{\begin{array}{c}x-y=1 \\ x-\frac{1}{2} y=4.5\end{array}\right.$
C. $\left\{\begin{array}{l}x-y=4.5 \\ y-\frac{1}{2} x=1\end{array}\right.$
D. $\left\{\begin{array}{l}x+y=4.5 \\ y-\frac{1}{2} x=1\end{array}\right.$