To determine which system of equations can be graphed to find the solution(s) to the equation [tex]\( x^2 = 2x + 3 \)[/tex], let's start by rewriting the given equation in a way that can help us identify the system of equations.
Given:
[tex]\[ x^2 = 2x + 3 \][/tex]
First, isolate one side of the equation to form a standard quadratic equation:
[tex]\[ x^2 - 2x - 3 = 0 \][/tex]
Now let’s consider the graphing approach. One way to graphically solve for [tex]\( x \)[/tex] is to express the original equation as two functions and see where they intersect.
Rewrite the equation in terms of two separate functions [tex]\( y \)[/tex]:
1. [tex]\( f_1(x) = x^2 \)[/tex]
2. [tex]\( f_2(x) = 2x + 3 \)[/tex]
So the system of equations becomes:
[tex]\[
\begin{cases}
y = x^2 \\
y = 2x + 3
\end{cases}
\][/tex]
Thus, to find the solution(s) to the equation [tex]\( x^2 = 2x + 3 \)[/tex], we can graph the following system of equations and find the points where these graphs intersect:
[tex]\[
\begin{cases}
y = x^2 \\
y = 2x + 3
\end{cases}
\][/tex]
This matches the last option provided:
[tex]\[
\begin{cases}
y = x^2 \\
y = 2x + 3
\end{cases}
\][/tex]
Therefore, the system of equations that can be graphed to find the solution(s) to [tex]\( x^2 = 2x + 3 \)[/tex] is:
[tex]\[
\begin{cases}
y = x^2 \\
y = 2x + 3
\end{cases}
\][/tex]
