Solve the system by the substitution method.
-$$\begin{array} { l }
x + y = - 5 \
( x - 2 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 20
\end{array}$$
A) $\{ ( - 2 , - 3 ) , ( 4 , - 9 ) \}$
B) $\{ ( - 3 , - 2 ) , ( - 9,4 ) \}$
C) $\{ ( - 2 , - 3 ) , ( 0 , - 9 ) \}$
D) $\{ ( - 3 , - 2 ) , ( - 9,0 ) \}$

Question

Solve the system by the substitution method.
-$$\begin{array} { l } 
x + y = - 5 \
( x - 2 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 20
\end{array}$$
A) $\{ ( - 2 , - 3 ) , ( 4 , - 9 ) \}$
B) $\{ ( - 3 , - 2 ) , ( - 9,4 ) \}$
C) $\{ ( - 2 , - 3 ) , ( 0 , - 9 ) \}$
D) $\{ ( - 3 , - 2 ) , ( - 9,0 ) \}$

Quizplus · Accepted Answer

To solve the system by substitution, we first solve the first equation for one of the variables, say $x$. From $x + y = -5$, we get $x = -5 - y$. Substituting $x = -5 - y$ into the second equation, we have $(-5 - y - 2)^2 + (y + 5)^2 = 20$, which simplifies to $(-7 - y)^2 + (y + 5)^2 = 20$. Expanding and simplifying this equation will give us a quadratic equation in terms of $y$. Solving this quadratic equation will give us the values of $y$, and substituting these values back into $x = -5 - y$ will give us the corresponding $x$ values. The correct pairs that satisfy both equations are $(-2, -3)$ and $(4, -9)$, making option A the correct choice.

Solve the System by the Substitution Method x+y=−5(x−2)2+(y+5)2=20\begin{array} { l } x + y = - 5 \\( x - 2 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 20\end{array}x+y=−5(x−2)2+(y+5)2=20​

Solve the System by the Substitution Method $\begin{array} { l } x + y = - 5 \\( x - 2 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 20\end{array}$