Give All Solutions of the Nonlinear System of Equations, Including $$\begin{array} { l } x ^ { 2 } + x y + y ^ { 2 } = 19 \\x + y = 2\end{array}$$

Multiple Choice

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
- $$\begin{array} { l } x ^ { 2 } + x y + y ^ { 2 } = 19 \\x + y = 2\end{array}$$

A) $\{ ( - 3,5 ) \}$
B) $\{ ( 5 , - 3 ) \}$
C) $\{ ( 5 , - 3 ) , ( - 3,5 ) \}$
D) $\{ ( 4 , - 2 ) , ( - 4,6 ) \}$