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

[tex]\[

\begin{array}{l}

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

y = 7x^4 + 2x

\end{array}

\][/tex]

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

B. [tex]$ 3x^3 - 7x^2 + 5 = 0 $[/tex]

C. [tex]$ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 $[/tex]

D. [tex]$ 7x^4 + 2x = 0 $[/tex]

To solve this problem, we're given two equations and four possible options for which a system of equations can be solved. Let's analyze the equations:

1. The given system of equations is:
- [tex]$ y = 3x^3 - 7x^2 + 5 $[/tex]
- [tex]$ y = 7x^4 + 2x $[/tex]

To find an equation that can be solved using this system, we need to set the two expressions for [tex]$ y $[/tex] equal to each other because they both represent the same [tex]$ y $[/tex]-value:

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

This equation is formed by equating the two given equations, as they both equal [tex]$ y $[/tex].

Now, let's analyze the options:

1. [tex]$ 3x^3 - 7x^2 + 5 = 7x^4 + 2x $[/tex]
2. [tex]$ 3x^3 - 7x^2 + 5 = 0 $[/tex]
3. [tex]$ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 $[/tex]
4. [tex]$ 7x^4 + 2x = 0 $[/tex]

Option 1 is exactly the equation we derived from setting the two expressions for [tex]$ y $[/tex] equal to each other:

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

Therefore, the equation that can be solved using the given system is Option 1: [tex]$ 3x^3 - 7x^2 + 5 = 7x^4 + 2x $[/tex].