Solve the Nonlinear System of Equations for Real Solutions $\left\{ \begin{array} { l } x ^ { 2 } + 3 y ^ { 2 } = 6 \\x ^ { 2 } - 3 y ^ { 2 } = 8\end{array} \right.$

Multiple Choice

Solve the nonlinear system of equations for real solutions.
- $\left\{ \begin{array} { l } x ^ { 2 } + 3 y ^ { 2 } = 6 \\x ^ { 2 } - 3 y ^ { 2 } = 8\end{array} \right.$

A) $( \sqrt { 7 } , 1 ) , ( \sqrt { 7 } , - 1 )$
B) $\varnothing$
C) $( \sqrt { 7 } , 1 ) , ( - \sqrt { 7 } , - 1 )$
D) $( \sqrt { 7 } , 1 ) , ( \sqrt { 7 } , - 1 ) , ( - \sqrt { 7 } , 1 ) , ( - \sqrt { 7 } , - 1 )$