Solve the nonlinear system of equations.
-$$\left\{ \begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 113 \
x + y = - 15
\end{array} \right.$$
A) $( 7 , - 8 ) , ( 8 , - 7 )$
B) $( - 7 , - 8 ) , ( - 8 , - 7 )$
C) $( 7,8 ) , ( 8,7 )$
D) $( - 7,8 ) , ( - 8,7 )$

Question

Solve the nonlinear system of equations.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 113 \
x + y = - 15
\end{array} \right.$$
A) $( 7 , - 8 ) , ( 8 , - 7 )$
B) $( - 7 , - 8 ) , ( - 8 , - 7 )$
C) $( 7,8 ) , ( 8,7 )$
D) $( - 7,8 ) , ( - 8,7 )$

Quizplus · Accepted Answer

To solve the system, we can use substitution or elimination. From the second equation, $y = -15 - x$. Substituting this into the first equation gives $x^2 + (-15 - x)^2 = 113$. Simplifying and solving for $x$ yields $x = -7$ or $x = -8$. Substituting these values back into $y = -15 - x$ gives the corresponding $y$ values, resulting in the solutions $(-7, -8)$ and $(-8, -7)$.

Solve the Nonlinear System of Equations {x2+y2=113x+y=−15\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 113 \\x + y = - 15\end{array} \right.{x2+y2=113x+y=−15​

Solve the Nonlinear System of Equations $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 113 \\x + y = - 15\end{array} \right.$