Solve the System of Nonlinear Equations by the Addition Method $$\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\2 x ^ { 2 } + y ^ { 2 } = 50\end{array}$$

Multiple Choice

Solve the system of nonlinear equations by the addition method. $$\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\2 x ^ { 2 } + y ^ { 2 } = 50\end{array}$$

A) $\{ ( 0,5 ) \}$
B) $\{ ( 5,0 ) \}$
C) $\{ ( - 5,0 ) , ( 5,0 ) \}$
D) $\{ ( 0 , - 5 ) , ( 0,5 ) \}$