Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l }
10 x ^ { 2 } + y ^ { 2 } = 100 \
10 x ^ { 2 } - y ^ { 2 } = 100
\end{array} \right.$
A) $( \sqrt { 10 } , 0 ) , ( - \sqrt { 10 } , 0 )$
B) $( 0,10 ) , ( 0 , - 10 )$
C) $( 0 , \sqrt { 10 } ) , ( 0 , - \sqrt { 10 } )$
D) $( 10,0 ) , ( - 10,0 )$

Question

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l } 
10 x ^ { 2 } + y ^ { 2 } = 100 \
10 x ^ { 2 } - y ^ { 2 } = 100
\end{array} \right.$
A) $( \sqrt { 10 } , 0 ) , ( - \sqrt { 10 } , 0 )$
B) $( 0,10 ) , ( 0 , - 10 )$
C) $( 0 , \sqrt { 10 } ) , ( 0 , - \sqrt { 10 } )$
D) $( 10,0 ) , ( - 10,0 )$

Quizplus · Accepted Answer

Adding the two equations gives $20x^2 = 200$, which simplifies to $x^2 = 10$, leading to $x = \sqrt{10}$ or $x = -\sqrt{10}$. Substituting $x$ back into either equation shows $y = 0$.

Solve the Nonlinear System of Equations for Real Solutions {10x2+y2=10010x2−y2=100\left\{ \begin{array} { l } 10 x ^ { 2 } + y ^ { 2 } = 100 \\10 x ^ { 2 } - y ^ { 2 } = 100\end{array} \right.{10x2+y2=10010x2−y2=100​

Solve the Nonlinear System of Equations for Real Solutions $\left\{ \begin{array} { l } 10 x ^ { 2 } + y ^ { 2 } = 100 \\10 x ^ { 2 } - y ^ { 2 } = 100\end{array} \right.$