Solve Nonlinear Systems By Addition
-$$\begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 65 \
( x - 1 ) ^ { 2 } + y ^ { 2 } = 64
\end{array}$$
A) $\{ ( 1,8 ) , ( 1 , - 8 ) \}$
B) $\{ ( 1,8 ) , ( 1 , - 8 ) , ( - 1,8 ) , ( - 1 , - 8 ) \}$
C) $\{ ( 8,1 ) , ( 8 , - 1 ) \}$
D) $\{ ( 8,1 ) , ( 8 , - 1 ) , ( - 8,1 ) , ( - 8 , - 1 ) \}$

Question

Solve Nonlinear Systems By Addition
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 65 \
( x - 1 ) ^ { 2 } + y ^ { 2 } = 64
\end{array}$$
A) $\{ ( 1,8 ) , ( 1 , - 8 ) \}$
B) $\{ ( 1,8 ) , ( 1 , - 8 ) , ( - 1,8 ) , ( - 1 , - 8 ) \}$
C) $\{ ( 8,1 ) , ( 8 , - 1 ) \}$
D) $\{ ( 8,1 ) , ( 8 , - 1 ) , ( - 8,1 ) , ( - 8 , - 1 ) \}$

Quizplus · Accepted Answer

Subtracting the second equation from the first gives $2x - 1 = 1$, solving for $x$ gives $x = 1$. Substituting $x = 1$ into either equation and solving for $y$ gives $y = \pm 8$.

Solve Nonlinear Systems by Addition - x2+y2=65(x−1)2+y2=64\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 65 \\( x - 1 ) ^ { 2 } + y ^ { 2 } = 64\end{array}x2+y2=65(x−1)2+y2=64​

Solve Nonlinear Systems by Addition
- $\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 65 \\( x - 1 ) ^ { 2 } + y ^ { 2 } = 64\end{array}$