College

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 are equal to [tex]$y$[/tex], we set them equal to each other:
[tex]$$
3x^3 - 7x^2 + 5 = 7x^4 + 2x.
$$[/tex]

This is the equation that is solved by the given system of equations. Therefore, the correct answer is the equation:
[tex]$$
3x^3 - 7x^2 + 5 = 7x^4 + 2x.
$$[/tex]

This corresponds to option 2.

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