Solve the nonlinear system of equations.
-$$\left\{ \begin{array} { l }
y = x ^ { 2 } + 8 \
y = - x ^ { 2 } + 10
\end{array} \right.$$
A) $( 1,9 ) , ( 1 , - 9 ) , ( - 1,9 ) , ( - 1 , - 9 )$
B) $( 9,1 ) , ( 9 , - 1 )$
C) $( 1,9 ) , ( - 1,9 )$
D) $\varnothing$

Question

Solve the nonlinear system of equations.
-$$\left\{ \begin{array} { l } 
y = x ^ { 2 } + 8 \
y = - x ^ { 2 } + 10
\end{array} \right.$$
A) $( 1,9 ) , ( 1 , - 9 ) , ( - 1,9 ) , ( - 1 , - 9 )$
B) $( 9,1 ) , ( 9 , - 1 )$
C) $( 1,9 ) , ( - 1,9 )$
D) $\varnothing$

Quizplus · Accepted Answer

To solve the system, set the two equations equal to each other: $x^2 + 8 = -x^2 + 10$. Solving for $x^2$, we get $x^2 = 1$, so $x = \pm 1$. Substituting $x = 1$ and $x = -1$ back into either equation gives $y = 9$. Therefore, the solutions are $(1, 9)$ and $(-1, 9)$.

Solve the Nonlinear System of Equations {y=x2+8y=−x2+10\left\{ \begin{array} { l } y = x ^ { 2 } + 8 \\y = - x ^ { 2 } + 10\end{array} \right.{y=x2+8y=−x2+10​

Solve the Nonlinear System of Equations $\left\{ \begin{array} { l } y = x ^ { 2 } + 8 \\y = - x ^ { 2 } + 10\end{array} \right.$