Solve the system by using any method.
-$$\begin{array} { l }
x ^ { 2 } + ( y - 4 ) ^ { 2 } = 16 \
y = - x ^ { 2 } + 8
\end{array}$$
A) $\{ ( 0,0 ) , ( - \sqrt { 7 } , 7 ) , ( \sqrt { 7 } , 7 ) \}$
B) $\{ ( 0,8 ) \}$
C) $\{ ( 0,0 ) \}$
D) $\{ ( 0,8 ) , ( - \sqrt { 7 } , 1 ) , ( \sqrt { 7 } , 1 ) \}$

Question

Solve the system by using any method.
-$$\begin{array} { l } 
x ^ { 2 } + ( y - 4 ) ^ { 2 } = 16 \
y = - x ^ { 2 } + 8
\end{array}$$
A) $\{ ( 0,0 ) , ( - \sqrt { 7 } , 7 ) , ( \sqrt { 7 } , 7 ) \}$
B) $\{ ( 0,8 ) \}$
C) $\{ ( 0,0 ) \}$
D) $\{ ( 0,8 ) , ( - \sqrt { 7 } , 1 ) , ( \sqrt { 7 } , 1 ) \}$

Quizplus · Accepted Answer

Substituting $y = -x^2 + 8$ into the first equation gives $x^2 + ((-x^2 + 8) - 4)^2 = 16$. Simplifying and solving this equation yields the solutions $(0,8)$, $(- \sqrt{7}, 1)$, and $(\sqrt{7}, 1)$.

Solve the System by Using Any Method x2+(y−4)2=16y=−x2+8\begin{array} { l } x ^ { 2 } + ( y - 4 ) ^ { 2 } = 16 \\y = - x ^ { 2 } + 8\end{array}x2+(y−4)2=16y=−x2+8​

Solve the System by Using Any Method $\begin{array} { l } x ^ { 2 } + ( y - 4 ) ^ { 2 } = 16 \\y = - x ^ { 2 } + 8\end{array}$