To determine which system of equations can be graphed to find the solutions to [tex]\( x^2 = 2x + 3 \)[/tex], we need to express the original equation in a format that can be compared graphically:
1. We start with the equation [tex]\( x^2 = 2x + 3 \)[/tex].
2. We need to rewrite this equation in the standard form [tex]\( y = f(x) \)[/tex] for both graphs that we want to solve for intersections.
3. Subtract [tex]\( 2x + 3 \)[/tex] from both sides to get the equation in [tex]\( y = 0 \)[/tex] form:
[tex]\[ x^2 - 2x - 3 = 0 \][/tex]
4. Now, we separate this into two functions to form a system of equations:
- Let [tex]\( y = x^2 - 2x - 3 \)[/tex]
- And let [tex]\( y = 2x + 3 \)[/tex]
Thus, the system of equations that can be graphed to find the solution(s) to [tex]\( x^2 = 2x + 3 \)[/tex] is:
[tex]\[
\left\{
\begin{array}{l}
y = x^2 - 2x - 3 \\
y = 2x + 3
\end{array}
\right.
\][/tex]
So, the correct answer is:
[tex]\[
\left\{
\begin{array}{l}
y = x^2 - 2x - 3 \\
y = 2x + 3
\end{array}
\right.
\][/tex]
