Solve Nonlinear Systems By Addition
Solve the system by the addition method.
-$$\begin{array} { l }
x ^ { 2 } + y ^ { 2 } - 4 x + 8 y + 19 = 0 \
x ^ { 2 } - y ^ { 2 } - 4 x - 8 y - 13 = 0
\end{array}$$
A) $\{ ( 3 , - 4 ) , ( 1 , - 4 ) \}$
B) $\{ ( 3 , - 4 ) , ( - 1 , - 4 ) \}$
C) $\{ ( 2 , - 3 ) , ( 2 , - 5 ) \}$
D) $\{ ( 2,3 ) , ( 2,5 ) \}$ Solve by the method of your choice.

Question

Solve Nonlinear Systems By Addition
Solve the system by the addition method.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } - 4 x + 8 y + 19 = 0 \
x ^ { 2 } - y ^ { 2 } - 4 x - 8 y - 13 = 0
\end{array}$$
A) $\{ ( 3 , - 4 ) , ( 1 , - 4 ) \}$
B) $\{ ( 3 , - 4 ) , ( - 1 , - 4 ) \}$
C) $\{ ( 2 , - 3 ) , ( 2 , - 5 ) \}$
D) $\{ ( 2,3 ) , ( 2,5 ) \}$ Solve by the method of your choice.

Quizplus · Accepted Answer

By adding the two equations, the $y^2$ terms cancel out, simplifying the system to solve for $x$ and $y$. Solving gives the solutions $(3, -4)$ and $(1, -4)$.

Solve Nonlinear Systems by Addition Solve the System by the Addition

Solve Nonlinear Systems by Addition
Solve the System by the Addition