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Which equation can be solved by using this system of equations?

[tex]\[

\begin{cases}

y = 3x^3 - 7x^2 + 5 \\

y = 7x^4 + 2x

\end{cases}

\][/tex]

A. [tex]\(3x^3 - 7x^2 + 5 = 0\)[/tex]

B. [tex]\(3x^3 - 7x^2 + 5 = 7x^4 + 2x\)[/tex]

C. [tex]\(7x^4 + 2x = 0\)[/tex]

D. [tex]\(7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0\)[/tex]

Answer :

We start with the system of equations:

[tex]$$
\begin{cases}
y = 3x^3 - 7x^2 + 5, \\
y = 7x^4 + 2x.
\end{cases}
$$[/tex]

Since both expressions equal [tex]$y$[/tex], the intersection of the graphs occurs when their right-hand sides are equal. Therefore, we set:

[tex]$$
3x^3 - 7x^2 + 5 = 7x^4 + 2x.
$$[/tex]

This is the equation that must be solved to find the values of [tex]$x$[/tex] where the two curves meet.

Among the given options, the equation

[tex]$$
3x^3 - 7x^2 + 5 = 7x^4 + 2x
$$[/tex]

matches exactly with option 2.

Thus, the correct answer is [tex]$\boxed{2}$[/tex].

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