Solve Nonlinear Systems By Substitution
-$$\begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 25 \
x + y = - 7
\end{array}$$
A) $\{ ( - 3 , - 4 ) , ( - 4 , - 3 ) \}$
B) $\{ ( 3 , - 4 ) , ( 4 , - 3 ) \}$
C) $\{ ( - 3,4 ) , ( - 4,3 ) \}$
D) $\{ ( 3,4 ) , ( 4,3 ) \}$

Question

Solve Nonlinear Systems By Substitution
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 25 \
x + y = - 7
\end{array}$$
A) $\{ ( - 3 , - 4 ) , ( - 4 , - 3 ) \}$
B) $\{ ( 3 , - 4 ) , ( 4 , - 3 ) \}$
C) $\{ ( - 3,4 ) , ( - 4,3 ) \}$
D) $\{ ( 3,4 ) , ( 4,3 ) \}$

Quizplus · Accepted Answer

From the second equation, $y = -7 - x$. Substituting this into the first equation gives $x^2 + (-7 - x)^2 = 25$, which simplifies and solves to give the solutions $x = -3, y = -4$ and $x = -4, y = -3$, matching choice A.

Solve Nonlinear Systems by Substitution - x2+y2=25x+y=−7\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\x + y = - 7\end{array}x2+y2=25x+y=−7​

Solve Nonlinear Systems by Substitution
- $\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\x + y = - 7\end{array}$