Give All Solutions of the Nonlinear System of Equations, Including $\begin{array} { r } x y = 7 \\2 y ^ { 2 } - x ^ { 2 } = 7\end{array}$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { r } x y = 7 \\2 y ^ { 2 } - x ^ { 2 } = 7\end{array}$

A) $\left\{ \left( \mathrm { i } \sqrt { 14 } , - \frac { \mathrm { i } \sqrt { 14 } } { 2 } \right) , \left( - \mathrm { i } \sqrt { 14 } , \frac { \mathrm { i } \sqrt { 14 } } { 2 } \right) , ( \sqrt { 7 } , \sqrt { 7 } ) , ( - \sqrt { 7 } , - \sqrt { 7 } ) \right\}$
B) $\left. \left\{ - 14 , - \frac { 1 } { 2 } \right) , ( 7,1 ) \right\}$
C) $\left. \left\{ \mathrm { i } \sqrt { 14 } , - \frac { \mathrm { i } \sqrt { 14 } } { 2 } \right) , ( \sqrt { 7 } , \sqrt { 7 } ) \right\}$
D) $\{ ( 2 \mathrm { i } \sqrt { 7 } , - \mathrm { i } \sqrt { 7 } ) , ( - 2 \mathrm { i } \sqrt { 7 } , \mathrm { i } \sqrt { 7 } ) , ( \sqrt { 7 } , \sqrt { 7 } ) , ( - \sqrt { 7 } , - \sqrt { 7 } ) \}$

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