Solve the system of nonlinear equations by the addition method. $$\begin{array} { l }
7 y = - x + 7 \
x ^ { 2 } + 49 y ^ { 2 } = 49
\end{array}$$
A){ }
B) $\{ ( 7,0 ) ( 0 , - 1 ) \}$
C) $\{ ( - 7,0 ) ( 0 , - 1 ) \}$
D) $\{ ( 7,0 ) ( 0,1 ) \}$

Question

Solve the system of nonlinear equations by the addition method. $$\begin{array} { l } 
7 y = - x + 7 \
x ^ { 2 } + 49 y ^ { 2 } = 49
\end{array}$$
A){ }
B) $\{ ( 7,0 ) ( 0 , - 1 ) \}$
C) $\{ ( - 7,0 ) ( 0 , - 1 ) \}$
D) $\{ ( 7,0 ) ( 0,1 ) \}$

Quizplus · Accepted Answer

From the first equation, we can express $y$ in terms of $x$ as $y = \frac{-x + 7}{7}$. Substituting this into the second equation gives $x^2 + 49\left(\frac{-x + 7}{7}\right)^2 = 49$, which simplifies to $x^2 + (-x + 7)^2 = 49$. Solving this system yields the solutions $(7,0)$ and $(0,1)$.

Solve the System of Nonlinear Equations by the Addition Method 7y=−x+7x2+49y2=49\begin{array} { l } 7 y = - x + 7 \\x ^ { 2 } + 49 y ^ { 2 } = 49\end{array}7y=−x+7x2+49y2=49​

Solve the System of Nonlinear Equations by the Addition Method $\begin{array} { l } 7 y = - x + 7 \\x ^ { 2 } + 49 y ^ { 2 } = 49\end{array}$