Solve the system by the substitution method.
-$$\begin{array} { l }
2 x ^ { 2 } + 4 y ^ { 2 } = 36 \
y = x + 3
\end{array}$$
A) $\{ ( 0,3 ) , ( - 4 , - 1 ) \}$
B) $\{ ( 0 , - 3 ) , ( - 4 , - 1 ) \}$
C) $\{ [ 0,3 ) , ( 4,7 ) \}$
D) $\{ ( 0 , - 3 ) , ( 4,7 ) \}$

Question

Solve the system by the substitution method.
-$$\begin{array} { l } 
2 x ^ { 2 } + 4 y ^ { 2 } = 36 \
y = x + 3
\end{array}$$
A) $\{ ( 0,3 ) , ( - 4 , - 1 ) \}$
B) $\{ ( 0 , - 3 ) , ( - 4 , - 1 ) \}$
C) $\{ [ 0,3 ) , ( 4,7 ) \}$
D) $\{ ( 0 , - 3 ) , ( 4,7 ) \}$

Quizplus · Accepted Answer

Substitute $y = x + 3$ into the first equation: $2x^2 + 4(x + 3)^2 = 36$. Simplify and solve for $x$, then use $y = x + 3$ to find corresponding $y$ values. The solutions are $(0,3)$ and $(-4,-1)$.

Solve the System by the Substitution Method 2x2+4y2=36y=x+3\begin{array} { l } 2 x ^ { 2 } + 4 y ^ { 2 } = 36 \\y = x + 3\end{array}2x2+4y2=36y=x+3​

Solve the System by the Substitution Method $\begin{array} { l } 2 x ^ { 2 } + 4 y ^ { 2 } = 36 \\y = x + 3\end{array}$