Solve the system of equations.
-$$\begin{array} { l }
\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1 \
y = - x ^ { 2 } + 4
\end{array}$$
A) $\{ ( 0,4 ) , ( - 2,0 ) , ( 2,0 ) \}$
B) $\{ ( 0 , - 4 ) , ( - 2,0 ) , ( 2,0 ) \}$
C) $\{ ( 0,4 ) , ( 2,0 ) \}$
D) $\{ ( 0 , - 4 ) , ( 0,4 ) , ( - 2,0 ) , ( 2,0 ) \}$

Question

Solve the system of equations.
-$$\begin{array} { l } 
\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1 \
y = - x ^ { 2 } + 4
\end{array}$$
A) $\{ ( 0,4 ) , ( - 2,0 ) , ( 2,0 ) \}$
B) $\{ ( 0 , - 4 ) , ( - 2,0 ) , ( 2,0 ) \}$
C) $\{ ( 0,4 ) , ( 2,0 ) \}$
D) $\{ ( 0 , - 4 ) , ( 0,4 ) , ( - 2,0 ) , ( 2,0 ) \}$

Quizplus · Accepted Answer

Substitute $y = -x^2 + 4$ into the first equation to get $\frac{x^2}{4} + \frac{(-x^2 + 4)^2}{16} = 1$. Solve this equation to find the values of $x$ and then use $y = -x^2 + 4$ to find the corresponding $y$ values, resulting in the points $(0,4)$, $(-2,0)$, and $(2,0)$.

Solve the System of Equations x24+y216=1y=−x2+4\begin{array} { l } \frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1 \\y = - x ^ { 2 } + 4\end{array}4x2​+16y2​=1y=−x2+4​

Solve the System of Equations $\begin{array} { l } \frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1 \\y = - x ^ { 2 } + 4\end{array}$