AMC 10 2021-fall-a Problem 14

How many ordered pairs $(x,y)$ of real numbers satisfy the following system of equations? \begin{align*} x^2+3y&=9 \ (|x|+|y|-4)^2 &= 1 \end{align*} $\textbf{(A) } 1 \textbf{(B) } 2 \textbf{(C) } 3 \textbf{(D) } 5 \textbf{(E) } 7$