Answer :
We start with the system of equations:
$$
\begin{cases}
y = 3x^3 - 7x^2 + 5, \\
y = 7x^4 + 2x.
\end{cases}
$$
Since both expressions equal $y$, they must be equal to each other. Therefore, we set:
$$
3x^3 - 7x^2 + 5 = 7x^4 + 2x.
$$
This is the equation that can be solved to find the common $x$-values (the $x$-coordinates where the graphs of these equations intersect).
By comparing with the given options, we see that it corresponds to the second equation.
Thus, the answer is option 2:
$$
3x^3 - 7x^2 + 5 = 7x^4 + 2x.
$$
$$
\begin{cases}
y = 3x^3 - 7x^2 + 5, \\
y = 7x^4 + 2x.
\end{cases}
$$
Since both expressions equal $y$, they must be equal to each other. Therefore, we set:
$$
3x^3 - 7x^2 + 5 = 7x^4 + 2x.
$$
This is the equation that can be solved to find the common $x$-values (the $x$-coordinates where the graphs of these equations intersect).
By comparing with the given options, we see that it corresponds to the second equation.
Thus, the answer is option 2:
$$
3x^3 - 7x^2 + 5 = 7x^4 + 2x.
$$
