Solve the system of nonlinear equations by the addition method. $$\begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 25 \
2 x ^ { 2 } + y ^ { 2 } = 50
\end{array}$$
A) $\{ ( 0,5 ) \}$
B) $\{ ( 5,0 ) \}$
C) $\{ ( - 5,0 ) , ( 5,0 ) \}$
D) $\{ ( 0 , - 5 ) , ( 0,5 ) \}$

Question

Solve the system of nonlinear equations by the addition method. $$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 25 \
2 x ^ { 2 } + y ^ { 2 } = 50
\end{array}$$
A) $\{ ( 0,5 ) \}$
B) $\{ ( 5,0 ) \}$
C) $\{ ( - 5,0 ) , ( 5,0 ) \}$
D) $\{ ( 0 , - 5 ) , ( 0,5 ) \}$

Quizplus · Accepted Answer

Subtracting the first equation from the second gives $x^2 = 25$, leading to $x = \pm 5$. Substituting $x$ back into either equation shows $y = 0$, resulting in the solutions $(-5, 0)$ and $(5, 0)$.

Solve the System of Nonlinear Equations by the Addition Method x2+y2=252x2+y2=50\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\2 x ^ { 2 } + y ^ { 2 } = 50\end{array}x2+y2=252x2+y2=50​

Solve the System of Nonlinear Equations by the Addition Method $\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\2 x ^ { 2 } + y ^ { 2 } = 50\end{array}$