Solve Nonlinear Systems by Addition
Solve the System by the Addition

Solve Nonlinear Systems By Addition
Solve the system by the addition method.
- $$2 x ^ { 2 } + x y - y ^ { 2 } = 3$$
$x ^ { 2 } + 2 x y + y ^ { 2 } = 3$

A) $\left. \left\{ \left( \frac { 2 \sqrt { 3 } } { 3 } , \frac { \sqrt { 3 } } { 3 } \right) , - \frac { 2 \sqrt { 3 } } { 3 } , - \frac { \sqrt { 3 } } { 3 } \right) \right\}$
B) $\left\{ \left( \frac { 2 \sqrt { 3 } } { 3 } , - \frac { \sqrt { 3 } } { 3 } \right) , \left( - \frac { 2 \sqrt { 3 } } { 3 } , \frac { \sqrt { 3 } } { 3 } \right) \right\}$
C) $\left\{ \left( \frac { - 2 } { 3 } , \frac { 1 } { 3 } \right) , \left( \frac { 2 \sqrt { 3 } } { 3 } , - \frac { 1 } { 3 } \right) \right\}$
D) $\left\{ \left( \frac { - 2 } { 3 } , - \frac { 1 } { 3 } \right) , \left( \frac { 2 \sqrt { 3 } } { 3 } , \frac { 1 } { 3 } \right) \right\}$