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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 :

To determine which equation can be solved by using the given system of equations, we need to understand what the system represents:

We have two equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]

Since both expressions represent [tex]\( y \)[/tex], we can set them equal to each other. This means we're looking for the values of [tex]\( x \)[/tex] where the two expressions give the same [tex]\( y \)[/tex] value:

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

Now let's review the choices to find which one matches this equation:

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

The equation [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex] matches directly with one of the choices listed. Therefore, this is the equation that can be solved using the system of equations provided.

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