Solve the system. $\left\{ \begin{array} { l }
y = x ^ { 2 } - 25 \
y - 5 = x
\end{array} \right.$
A) $( - 5,0 ) , ( 5,11 )$
B) $( - 5,0 ) , ( 6,11 )$
C) $( - 6,11 ) , ( 6,11 )$
D) $( - 5,6 ) , ( 0,11 )$
E) $( 5,0 ) , ( - 6,0 )$

Question

Solve the system. $\left\{ \begin{array} { l } 
y = x ^ { 2 } - 25 \
y - 5 = x
\end{array} \right.$
A) $( - 5,0 ) , ( 5,11 )$
B) $( - 5,0 ) , ( 6,11 )$
C) $( - 6,11 ) , ( 6,11 )$
D) $( - 5,6 ) , ( 0,11 )$
E) $( 5,0 ) , ( - 6,0 )$

Quizplus · Accepted Answer

Using the second equation, we know that $y=x+5$. Substituting this into the first equation gives $x^2-25=x+5$, or $x^2-x-30=0$. Factoring, we get $(x-6)(x+5)=0$, so $x=6$ or $x=-5$. Plugging these values back into $y=x+5$ gives $y=11$ and $y=0$, respectively. Therefore, the solutions are $(6,11)$ and $(-5,0)$. Thus, the answer is B.

Solve the System {y=x2−25y−5=x\left\{ \begin{array} { l } y = x ^ { 2 } - 25 \\y - 5 = x\end{array} \right.{y=x2−25y−5=x​

Solve the System $\left\{ \begin{array} { l } y = x ^ { 2 } - 25 \\y - 5 = x\end{array} \right.$