Question

graph each equation of the system. then solve the system to find the points of intersection.\

$$\begin{cases}y = x^2 + 6\\\\y = 2x + 6\\end{cases}$$

\dots\
use the graphing tool to graph the system.\
click to enlarge graph\
list all the solutions. select the correct choice below and fill in any answer boxes in your choice\
\bigcirc a.\
the graphs intersect at \
(type an ordered pair. use a comma to separate answers as needed.)\
\bigcirc b.\
there is no solution.

Explanation:

Step1: Set equations equal

Since \( y = x^2 + 6 \) and \( y = 2x + 6 \), set \( x^2 + 6 = 2x + 6 \).

Step2: Solve for x

Subtract \( 2x + 6 \) from both sides: \( x^2 - 2x = 0 \). Factor: \( x(x - 2) = 0 \). So \( x = 0 \) or \( x = 2 \).

Step3: Find corresponding y

For \( x = 0 \), \( y = 2(0) + 6 = 6 \). For \( x = 2 \), \( y = 2(2) + 6 = 10 \).

Answer:

A. The graphs intersect at \((0, 6)\), \((2, 10)\)