如图，将正方形ABCD的一角折叠，折痕为AE，∠BAD比大∠BAE大48°．设∠BAD和∠BAE的度数分别为x、y，那么x、y所适合的一个方程组是（　　）

A：$\left\{\begin{array}{c}y-x=48\\ y+x=90\end{array}\right.$

B：$\left\{\begin{array}{c}y-x=48\\ y=2x\end{array}\right.$

C：$\left\{\begin{array}{c}y-x=48\\ y+2x=90\end{array}\right.$

D：$\left\{\begin{array}{c}x-y=48\\ x+2y=90\end{array}\right.$