Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 50 \
( x - 2 ) ^ { 2 } + y ^ { 2 } = 50
\end{array}$$
A) $( 1,7 ) , ( 1 , - 7 ) , ( - 1,7 ) , ( - 1 , - 7 )$
B) $( 7,1 ) , ( 7 , - 1 )$
C) $( 7,1 ) , ( 7 , - 1 ) , ( - 7,1 ) , ( - 7 , - 1 )$
D) $( 1,7 ) , ( 1 , - 7 )$

Question

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 50 \
( x - 2 ) ^ { 2 } + y ^ { 2 } = 50
\end{array}$$
A) $( 1,7 ) , ( 1 , - 7 ) , ( - 1,7 ) , ( - 1 , - 7 )$
B) $( 7,1 ) , ( 7 , - 1 )$
C) $( 7,1 ) , ( 7 , - 1 ) , ( - 7,1 ) , ( - 7 , - 1 )$
D) $( 1,7 ) , ( 1 , - 7 )$

Quizplus · Accepted Answer

Subtracting the second equation from the first eliminates $y^2$ and simplifies to $x=1$, leaving $y$ to be determined from the original equations as $y = \pm 7$.

Determine the Real Solutions to the System of Nonlinear Equations x2+y2=50(x−2)2+y2=50\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 50 \\( x - 2 ) ^ { 2 } + y ^ { 2 } = 50\end{array}x2+y2=50(x−2)2+y2=50​

Determine the Real Solutions to the System of Nonlinear Equations $\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 50 \\( x - 2 ) ^ { 2 } + y ^ { 2 } = 50\end{array}$