To identify which system of equations can be graphed to find the solution(s) to [tex]\(4x^2 = x^2 + 7\)[/tex], we need to follow these steps:
1. Rearrange the given equation:
[tex]\[
4x^2 = x^2 + 7
\][/tex]
By rearranging, we subtract [tex]\(x^2\)[/tex] from both sides:
[tex]\[
4x^2 - x^2 = 7
\][/tex]
This simplifies to:
[tex]\[
3x^2 = 7
\][/tex]
2. Express the given equation as two separate equations:
We can rewrite the rearranged equation [tex]\(3x^2 = 7\)[/tex] using function notation. Essentially, we want two functions [tex]\(y\)[/tex] which form the equality:
[tex]\[
y = 4x^2 \quad \text{and} \quad y = x^2 + 7
\][/tex]
3. Select the correct system of equations:
Looking at the systems provided, we compare:
- [tex]\(\left\{\begin{array}{l}y = 3x^2 \\ y = x^2 + 7\end{array}\right.\)[/tex]
- [tex]\(\left\{\begin{array}{l}y = 3x^2 + 7 \\ y = x^2 + 7\end{array}\right.\)[/tex]
- [tex]\(\left\{\begin{array}{l}y = 4x^2 \\ y = x^2 + 7\end{array}\right.\)[/tex]
- [tex]\(\left\{\begin{array}{l}y = 4x^2 \\ y = 4x^2 + 7\end{array}\right.\)[/tex]
The system that matches [tex]\(y = 4x^2\)[/tex] and [tex]\(y = x^2 + 7\)[/tex] is:
[tex]\[
\left\{\begin{array}{l}
y = 4x^2 \\
y = x^2 + 7
\end{array}\right.
\][/tex]
Thus, the system of equations that can be graphed to find the solution to [tex]\(4x^2 = x^2 + 7\)[/tex] is:
[tex]\(\boxed{\left\{\begin{array}{l}y=4 x^2 \\ y=x^2+7\end{array}\right.}\)[/tex]
