Solve Nonlinear Systems By Addition
Solve the system by the addition method.
-$$\begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 40 \
- 13 x + y ^ { 2 } = 82
\end{array}$$
A) $\{ ( - 6,2 ) , ( - 6 , - 2 ) \}$
B) $\{ ( - 6,2 ) \}$
C) $\{ ( - 6,2 ) , ( - 6 , - 2 ) , ( - 7,2 ) , ( - 7 , - 2 ) \}$
D) $\{ ( - 6,2 ) , ( - 6 , - 2 ) , ( 6,2 ) , ( 6 , - 2 ) \}$

Question

Solve Nonlinear Systems By Addition
Solve the system by the addition method.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 40 \
- 13 x + y ^ { 2 } = 82
\end{array}$$
A) $\{ ( - 6,2 ) , ( - 6 , - 2 ) \}$
B) $\{ ( - 6,2 ) \}$
C) $\{ ( - 6,2 ) , ( - 6 , - 2 ) , ( - 7,2 ) , ( - 7 , - 2 ) \}$
D) $\{ ( - 6,2 ) , ( - 6 , - 2 ) , ( 6,2 ) , ( 6 , - 2 ) \}$

Quizplus · Accepted Answer

To solve the system, subtract the second equation from the first: $x^2 + y^2 - (-13x + y^2) = 40 - 82$, simplifying to $x^2 + 13x - 42 = 0$. Factoring gives $(x + 6)(x - 7) = 0$, so $x = -6$ or $x = 7$. Substituting $x = -6$ into the first equation gives $36 + y^2 = 40$, so $y^2 = 4$, and $y = \pm 2$. However, substituting $x = 7$ does not satisfy the original system, leaving $(-6, 2)$ and $(-6, -2)$ as the correct solutions.

Solve Nonlinear Systems by Addition Solve the System by the Addition

Solve Nonlinear Systems by Addition
Solve the System by the Addition