Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l }
x ^ { 2 } - y ^ { 2 } = 15 \
x ^ { 2 } + y ^ { 2 } = 21
\end{array} \right.$
A) $\varnothing$
B) $( - 3 \sqrt { 2 } , - \sqrt { 3 } )$
C) $( 3 \sqrt { 2 } , \sqrt { 3 } ) , ( - 3 \sqrt { 2 } , \sqrt { 3 } )$
D) $( 3 \sqrt { 2 } , \sqrt { 3 } ) , ( - 3 \sqrt { 2 } , \sqrt { 3 } ) , ( 3 \sqrt { 2 } , - \sqrt { 3 } ) , ( - 3 \sqrt { 2 } , - \sqrt { 3 } )$

Question

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 15 \
x ^ { 2 } + y ^ { 2 } = 21
\end{array} \right.$
A) $\varnothing$
B) $( - 3 \sqrt { 2 } , - \sqrt { 3 } )$
C) $( 3 \sqrt { 2 } , \sqrt { 3 } ) , ( - 3 \sqrt { 2 } , \sqrt { 3 } )$
D) $( 3 \sqrt { 2 } , \sqrt { 3 } ) , ( - 3 \sqrt { 2 } , \sqrt { 3 } ) , ( 3 \sqrt { 2 } , - \sqrt { 3 } ) , ( - 3 \sqrt { 2 } , - \sqrt { 3 } )$

Quizplus · Accepted Answer

Adding the two equations gives $2x^2 = 36$, leading to $x = \pm 3\sqrt{2}$. Substituting $x$ back into one of the equations gives $y = \pm \sqrt{3}$.

Solve the Nonlinear System of Equations for Real Solutions {x2−y2=15x2+y2=21\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 15 \\x ^ { 2 } + y ^ { 2 } = 21\end{array} \right.{x2−y2=15x2+y2=21​

Solve the Nonlinear System of Equations for Real Solutions $\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 15 \\x ^ { 2 } + y ^ { 2 } = 21\end{array} \right.$