Solve the system by the substitution method.
-$$\begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 37 \
y = \sqrt { x - 5 }
\end{array}$$
A) $\{ ( - 7 , - 12 ) \}$
B) $\{ ( - 7 , - 12 ) , ( 6,1 ) \}$
C) \{ \}
D) $\{ ( 6,1 ) \}$

Question

Solve the system by the substitution method.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 37 \
y = \sqrt { x - 5 }
\end{array}$$
A) $\{ ( - 7 , - 12 ) \}$
B) $\{ ( - 7 , - 12 ) , ( 6,1 ) \}$
C) \{ \}
D) $\{ ( 6,1 ) \}$

Quizplus · Accepted Answer

Substitute $y = \sqrt{x - 5}$ into the first equation: $x^2 + (\sqrt{x - 5})^2 = 37$. Simplify to $x^2 + x - 5 = 37$, leading to $x^2 + x - 42 = 0$. Factoring gives $(x + 7)(x - 6) = 0$, so $x = -7$ or $x = 6$. When $x = -7$, $y = \sqrt{-7 - 5}$ is not real. When $x = 6$, $y = \sqrt{6 - 5} = 1$. Thus, the solution is $\{(6,1)\}$.

Solve the System by the Substitution Method x2+y2=37y=x−5\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 37 \\y = \sqrt { x - 5 }\end{array}x2+y2=37y=x−5​​

Solve the System by the Substitution Method $\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 37 \\y = \sqrt { x - 5 }\end{array}$