Solve the Nonlinear System of Equations for Real Solutions $\left\{ \begin{array} { l } 10 x ^ { 2 } + y ^ { 2 } = 100 \\10 x ^ { 2 } - y ^ { 2 } = 100\end{array} \right.$

Multiple Choice

Solve the nonlinear system of equations for real solutions.
- $\left\{ \begin{array} { l } 10 x ^ { 2 } + y ^ { 2 } = 100 \\10 x ^ { 2 } - y ^ { 2 } = 100\end{array} \right.$

A) $( \sqrt { 10 } , 0 ) , ( - \sqrt { 10 } , 0 )$
B) $( 0,10 ) , ( 0 , - 10 )$
C) $( 0 , \sqrt { 10 } ) , ( 0 , - \sqrt { 10 } )$
D) $( 10,0 ) , ( - 10,0 )$