Give All Solutions of the Nonlinear System of Equations, Including $$\begin{array} { r } 5 x ^ { 2 } + 3 x y - 5 y ^ { 2 } = - 9 \\x ^ { 2 } - x y - y ^ { 2 } = - 5\end{array}$$

Multiple Choice

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
- $$\begin{array} { r } 5 x ^ { 2 } + 3 x y - 5 y ^ { 2 } = - 9 \\x ^ { 2 } - x y - y ^ { 2 } = - 5\end{array}$$

A) $\{ ( - 1 , - 2 ) , ( 1,2 ) , ( 2 \mathrm { i } , - \mathrm { i } ) , ( - 2 \mathrm { i } , \mathrm { i } ) \}$
B) $\left\{ ( - 1,2 ) , ( 1 , - 2 ) , \left( 2 \mathrm { i } \sqrt { 2 } , \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) , \left( - 2 \mathrm { i } \sqrt { 2 } , - \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) \right\}$
C) $\left\{ ( - 1 , - 2 ) , ( 1,2 ) , \left( 2 \mathrm { i } \sqrt { 2 } , - \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) , \left( - 2 \mathrm { i } \sqrt { 2 } , \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) \right\}$
D) $\{ ( - 1,2 ) , ( 1 , - 2 ) , ( 2 \mathrm { i } , \mathrm { i } ) , ( - 2 \mathrm { i } , - \mathrm { i } ) \}$