Determine the Real Solutions to the System of Nonlinear Equations $$\begin{array} { l } 4 x ^ { 2 } + y ^ { 2 } = 16 \\4 x ^ { 2 } - y ^ { 2 } = 16\end{array}$$

Multiple Choice

Determine the real solutions to the system of nonlinear equations.
- $$\begin{array} { l } 4 x ^ { 2 } + y ^ { 2 } = 16 \\4 x ^ { 2 } - y ^ { 2 } = 16\end{array}$$

A) $( 2,0 ) , ( - 2,0 )$
B) $( 0,2 ) , ( 0 , - 2 )$
C) $( 4,0 ) , ( - 4,0 )$
D) $( 0,4 ) , ( 0 , - 4 )$