Choose the one alternative that best completes the statement or answers the question.
-$$\left\{ \begin{array} { l }
2 x ^ { 2 } + x y - y ^ { 2 } = 3 \
x ^ { 2 } + 2 x y + y ^ { 2 } = 3
\end{array} \right.$$
A) $x = - \frac { 2 } { 3 } , y = \frac { 1 } { 3 } ; x = \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { 1 } { 3 }$
B) $x = \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { \sqrt { 3 } } { 3 } ; x = - \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { \sqrt { 3 } } { 3 }$
C) $x = - \frac { 2 } { 3 } , y = - \frac { 1 } { 3 } ; x = \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { 1 } { 3 }$
D) $x = \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { \sqrt { 3 } } { 3 } ; x = - \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { \sqrt { 3 } } { 3 }$

Question

Choose the one alternative that best completes the statement or answers the question.
-$$\left\{ \begin{array} { l } 
2 x ^ { 2 } + x y - y ^ { 2 } = 3 \
x ^ { 2 } + 2 x y + y ^ { 2 } = 3
\end{array} \right.$$
A) $x = - \frac { 2 } { 3 } , y = \frac { 1 } { 3 } ; x = \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { 1 } { 3 }$
B) $x = \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { \sqrt { 3 } } { 3 } ; x = - \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { \sqrt { 3 } } { 3 }$
C) $x = - \frac { 2 } { 3 } , y = - \frac { 1 } { 3 } ; x = \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { 1 } { 3 }$
D) $x = \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { \sqrt { 3 } } { 3 } ; x = - \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { \sqrt { 3 } } { 3 }$

Quizplus · Accepted Answer

To solve the system of equations, we can add them together to eliminate the $xy$ term, resulting in a simpler equation that can be solved for $x$ and $y$. The correct solutions must satisfy both original equations, and option B provides the correct pairs of $x$ and $y$ that do so.

Choose the One Alternative That Best Completes the Statement or Answers