Solve the system by the substitution or elimination method. $$\left( \begin{array} { l }
y = - x ^ { 2 } + 38 \
y = x ^ { 2 } + 6
\end{array} \right)$$
A) ( $-$ 4, 22), (4, 22)
B) ( $-$ 4, 22), ( $-$ 4, $-$ 22)
C) (4, $-$ 22)
D) (4, $-$ 22), (4, 22)

Question

Solve the system by the substitution or elimination method. $$\left( \begin{array} { l } 
y = - x ^ { 2 } + 38 \
y = x ^ { 2 } + 6
\end{array} \right)$$
A) ( $-$ 4, 22), (4, 22)
B) ( $-$ 4, 22), ( $-$ 4, $-$ 22)
C) (4, $-$ 22)
D) (4, $-$ 22), (4, 22)

Quizplus · Accepted Answer

Since both equations are equal to $y$, set them equal to each other to solve for $x$: $-x^2 + 38 = x^2 + 6$. Solving this gives $x = \pm 4$. Substituting $x$ back into either equation to solve for $y$ gives $y = 22$. Therefore, the solutions are $(-4, 22)$ and $(4, 22)$.

Solve the System by the Substitution or Elimination Method (y=−x2+38y=x2+6)\left( \begin{array} { l } y = - x ^ { 2 } + 38 \\y = x ^ { 2 } + 6\end{array} \right)(y=−x2+38y=x2+6​)

Solve the System by the Substitution or Elimination Method $\left( \begin{array} { l } y = - x ^ { 2 } + 38 \\y = x ^ { 2 } + 6\end{array} \right)$