Give All Solutions of the Nonlinear System of Equations, Including $$x ^ { 2 } + 3 x y + y ^ { 2 } = 4$$

Multiple Choice

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

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