Give All Solutions of the Nonlinear System of Equations, Including $\begin{array} { l } x ^ { 2 } + 3 x y + y ^ { 2 } = 4 \\x ^ { 2 } - 3 x y - y ^ { 2 } = 4\end{array}$

Multiple Choice

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { l } x ^ { 2 } + 3 x y + y ^ { 2 } = 4 \\x ^ { 2 } - 3 x y - y ^ { 2 } = 4\end{array}$

A) {(0,2) ,(0,-2) ,(2,-6) ,(-2,6) }
B) {(2,-6) ,(-2,6) }
C) {(2,0) ,(-2,0) }
D) {(2,0) ,(-2,0) ,(2,-6) ,(-2,6) }