Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l }
3 x ^ { 2 } - 5 y ^ { 2 } = 28 \
4 x ^ { 2 } + 3 y ^ { 2 } = 76
\end{array} \right.$
A) $( - 4 , - 2 ) , ( - 2 , - 4 )$
B) $( 4 , - 2 ) , ( 4,2 )$
C) $( 4,2 ) , ( 2,4 ) , ( - 4 , - 2 ) , ( - 2 , - 4 )$
D) $( 4,2 ) , ( - 4,2 ) , ( 4 , - 2 ) , ( - 4 , - 2 )$

Question

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l } 
3 x ^ { 2 } - 5 y ^ { 2 } = 28 \
4 x ^ { 2 } + 3 y ^ { 2 } = 76
\end{array} \right.$
A) $( - 4 , - 2 ) , ( - 2 , - 4 )$
B) $( 4 , - 2 ) , ( 4,2 )$
C) $( 4,2 ) , ( 2,4 ) , ( - 4 , - 2 ) , ( - 2 , - 4 )$
D) $( 4,2 ) , ( - 4,2 ) , ( 4 , - 2 ) , ( - 4 , - 2 )$

Quizplus · Accepted Answer

To solve the system, add the two equations to eliminate $y^2$: $7x^2 = 104$, leading to $x^2 = 104/7$, so $x = \pm 4$. Substituting $x$ back into one of the original equations gives $y = \pm 2$. Thus, the solutions are $(4,2)$, $(-4,2)$, $(4,-2)$, and $(-4,-2)$.

Solve the Nonlinear System of Equations for Real Solutions {3x2−5y2=284x2+3y2=76\left\{ \begin{array} { l } 3 x ^ { 2 } - 5 y ^ { 2 } = 28 \\4 x ^ { 2 } + 3 y ^ { 2 } = 76\end{array} \right.{3x2−5y2=284x2+3y2=76​

Solve the Nonlinear System of Equations for Real Solutions $\left\{ \begin{array} { l } 3 x ^ { 2 } - 5 y ^ { 2 } = 28 \\4 x ^ { 2 } + 3 y ^ { 2 } = 76\end{array} \right.$