Solve the system by using any method.
-$\begin{array} { l }
( x + 2 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 25 \
( x - 3 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 8
\end{array}$

A) $\left\{ ( 1,1 ) , \left( \frac { 85 } { 61 } , \frac { 41 } { 61 } \right) \right\}$
B) $\left\{ \left( \frac { 85 } { 61 } , \frac { 41 } { 61 } \right) , \left( - \frac { 85 } { 61 } , - \frac { 41 } { 61 } \right) \right\}$
C) $\{ ( 1,1 ) , ( - 1 , - 1 ) \}$
D) $\{ ( 1,1 ) \}$

Question

Solve the system by using any method.
-$\begin{array} { l } 
( x + 2 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 25 \
( x - 3 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 8
\end{array}$

A) $\left\{ ( 1,1 ) , \left( \frac { 85 } { 61 } , \frac { 41 } { 61 } \right) \right\}$
B) $\left\{ \left( \frac { 85 } { 61 } , \frac { 41 } { 61 } \right) , \left( - \frac { 85 } { 61 } , - \frac { 41 } { 61 } \right) \right\}$
C) $\{ ( 1,1 ) , ( - 1 , - 1 ) \}$
D) $\{ ( 1,1 ) \}$

Quizplus · Accepted Answer

The system of equations represents two circles. Solving them involves finding their intersection points. The correct solution set includes the points $(1,1)$ and $\left(\frac{85}{61}, \frac{41}{61}\right)$, indicating that these are the points where the two circles intersect.

Solve the System by Using Any Method (x+2)2+(y+3)2=25(x−3)2+(y−3)2=8\begin{array} { l } ( x + 2 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 25 \\( x - 3 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 8\end{array}(x+2)2+(y+3)2=25(x−3)2+(y−3)2=8​

Solve the System by Using Any Method $\begin{array} { l } ( x + 2 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 25 \\( x - 3 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 8\end{array}$