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

Multiple Choice

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

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