Solve the system of equations.
-$$\begin{array} { l }
x ^ { 2 } + 4 y ^ { 2 } = 103 \
4 x ^ { 2 } - y ^ { 2 } = 4
\end{array}$$
A) $\{ ( \sqrt { 7 } , 2 \sqrt { 6 } ) , ( - \sqrt { 7 } , 2 \sqrt { 6 } ) , ( \sqrt { 7 } , - 2 \sqrt { 6 } ) , ( - \sqrt { 7 } , - 2 \sqrt { 6 } ) \}$
B) $\{ ( 7,24 ) , ( - 7,24 ) , ( 7 , - 24 ) , ( - 7 , - 24 ) \}$
C) $\{ ( 2 \sqrt { 6 } , \sqrt { 7 } ) , ( 2 \sqrt { 6 } , - \sqrt { 7 } ) , ( - 2 \sqrt { 6 } , \sqrt { 7 } ) , ( - 2 \sqrt { 6 } , - \sqrt { 7 } ) \}$
D) $\{ ( 24,7 ) , ( - 24,7 ) , ( 24 , - 7 ) , ( - 24 , - 7 ) \}$

Question

Solve the system of equations.
-$$\begin{array} { l } 
x ^ { 2 } + 4 y ^ { 2 } = 103 \
4 x ^ { 2 } - y ^ { 2 } = 4
\end{array}$$
A) $\{ ( \sqrt { 7 } , 2 \sqrt { 6 } ) , ( - \sqrt { 7 } , 2 \sqrt { 6 } ) , ( \sqrt { 7 } , - 2 \sqrt { 6 } ) , ( - \sqrt { 7 } , - 2 \sqrt { 6 } ) \}$
B) $\{ ( 7,24 ) , ( - 7,24 ) , ( 7 , - 24 ) , ( - 7 , - 24 ) \}$
C) $\{ ( 2 \sqrt { 6 } , \sqrt { 7 } ) , ( 2 \sqrt { 6 } , - \sqrt { 7 } ) , ( - 2 \sqrt { 6 } , \sqrt { 7 } ) , ( - 2 \sqrt { 6 } , - \sqrt { 7 } ) \}$
D) $\{ ( 24,7 ) , ( - 24,7 ) , ( 24 , - 7 ) , ( - 24 , - 7 ) \}$

Quizplus · Accepted Answer

By solving the system of equations, we find that the solutions for $x$ and $y$ are $\pm \sqrt{7}$ and $\pm 2\sqrt{6}$, respectively.

Solve the System of Equations x2+4y2=1034x2−y2=4\begin{array} { l } x ^ { 2 } + 4 y ^ { 2 } = 103 \\4 x ^ { 2 } - y ^ { 2 } = 4\end{array}x2+4y2=1034x2−y2=4​

Solve the System of Equations $\begin{array} { l } x ^ { 2 } + 4 y ^ { 2 } = 103 \\4 x ^ { 2 } - y ^ { 2 } = 4\end{array}$