Give All Solutions of the Nonlinear System of Equations, Including $$\begin{aligned}x ^ { 2 } - 3 y ^ { 2 } & = 1 \\4 x ^ { 2 } + 3 y ^ { 2 } & = 19\end{aligned}$$

Multiple Choice

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
- $$\begin{aligned}x ^ { 2 } - 3 y ^ { 2 } & = 1 \\4 x ^ { 2 } + 3 y ^ { 2 } & = 19\end{aligned}$$

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