Give All Solutions of the Nonlinear System of Equations, Including $$\begin{array} { c } x ^ { 2 } - x y + y ^ { 2 } = 3 \\2 x ^ { 2 } + x y + 2 y ^ { 2 } = 12\end{array}$$

Multiple Choice

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
- $$\begin{array} { c } x ^ { 2 } - x y + y ^ { 2 } = 3 \\2 x ^ { 2 } + x y + 2 y ^ { 2 } = 12\end{array}$$

A) $\{ ( 1,0 ) , ( - 1,0 ) \}$
B) $\{ ( 2,1 ) , ( 1,2 ) \}$
C) $\{ ( 2,0 ) , ( - 2,0 ) , ( 1,0 ) , ( - 1,0 ) \}$
D) $\{ ( 2,1 ) , ( - 2 , - 1 ) , ( 1,2 ) , ( - 1 , - 2 ) \}$