Solve the nonlinear system of equations.
-$$\left\{ \begin{array} { l }
5 x ^ { 2 } - 4 y ^ { 2 } = 64 \
4 x ^ { 2 } + 4 y ^ { 2 } = 80
\end{array} \right.$$
A) $( 4 , - 2 ) , ( 4,2 )$
B) $( 4,2 ) , ( 2,4 ) , ( - 4 , - 2 ) , ( - 2 , - 4 )$
C) $( - 4 , - 2 ) , ( - 2 , - 4 )$
D) $( 4,2 ) , ( - 4,2 ) , ( 4 , - 2 ) , ( - 4 , - 2 )$

Question

Solve the nonlinear system of equations.
-$$\left\{ \begin{array} { l } 
5 x ^ { 2 } - 4 y ^ { 2 } = 64 \
4 x ^ { 2 } + 4 y ^ { 2 } = 80
\end{array} \right.$$
A) $( 4 , - 2 ) , ( 4,2 )$
B) $( 4,2 ) , ( 2,4 ) , ( - 4 , - 2 ) , ( - 2 , - 4 )$
C) $( - 4 , - 2 ) , ( - 2 , - 4 )$
D) $( 4,2 ) , ( - 4,2 ) , ( 4 , - 2 ) , ( - 4 , - 2 )$

Quizplus · Accepted Answer

Adding the two equations eliminates $y^2$, leading to a simplified equation in $x^2$ that, when solved, gives $x = \pm 4$. Substituting $x$ back into either equation allows solving for $y$, resulting in $y = \pm 2$.

Solve the Nonlinear System of Equations {5x2−4y2=644x2+4y2=80\left\{ \begin{array} { l } 5 x ^ { 2 } - 4 y ^ { 2 } = 64 \\4 x ^ { 2 } + 4 y ^ { 2 } = 80\end{array} \right.{5x2−4y2=644x2+4y2=80​

Solve the Nonlinear System of Equations $\left\{ \begin{array} { l } 5 x ^ { 2 } - 4 y ^ { 2 } = 64 \\4 x ^ { 2 } + 4 y ^ { 2 } = 80\end{array} \right.$