Solve Nonlinear Systems By Addition
Solve the system by the addition method.
-$$\begin{array} { l }
y = x ^ { 2 } + 4 \
y = - x ^ { 2 } + 10
\end{array}$$
A) $\{ ( \sqrt { 3 } , 7 ) , ( - \sqrt { 3 } , 7 ) \}$
B) $\{ ( \sqrt { 3 } , 7 ) , ( \sqrt { 3 } , - 7 ) , ( - \sqrt { 3 } , 7 ) , ( - \sqrt { 3 } , - 7 ) \}$
C) $\{ ( 7 , \sqrt { 3 } ) , ( 7 , - \sqrt { 3 } ) \}$
D) $\{ ( \sqrt { 3 } , 7 ) , ( \sqrt { 3 } , - 7 ) \}$

Question

Solve Nonlinear Systems By Addition
Solve the system by the addition method.
-$$\begin{array} { l } 
y = x ^ { 2 } + 4 \
y = - x ^ { 2 } + 10
\end{array}$$
A) $\{ ( \sqrt { 3 } , 7 ) , ( - \sqrt { 3 } , 7 ) \}$
B) $\{ ( \sqrt { 3 } , 7 ) , ( \sqrt { 3 } , - 7 ) , ( - \sqrt { 3 } , 7 ) , ( - \sqrt { 3 } , - 7 ) \}$
C) $\{ ( 7 , \sqrt { 3 } ) , ( 7 , - \sqrt { 3 } ) \}$
D) $\{ ( \sqrt { 3 } , 7 ) , ( \sqrt { 3 } , - 7 ) \}$

Quizplus · Accepted Answer

To solve the system by addition, we add the two equations together:$$y = x^2 + 4$$$$y = -x^2 + 10$$$$2y = 14$$$$y = 7$$Substitute $y = 7$ into one of the original equations:$$7 = x^2 + 4$$$$x^2 = 3$$$$x = \pm \sqrt{3}$$Therefore, the solutions are $(\sqrt{3}, 7)$ and $(- \sqrt{3}, 7)$.

Solve Nonlinear Systems by Addition Solve the System by the Addition

Solve Nonlinear Systems by Addition
Solve the System by the Addition