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 :

To determine which equation can be solved by the given system of equations, let's analyze the system:

We have two equations:

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

Since both equations represent [tex]\( y \)[/tex], we can find when they are equal to each other by setting them equal:

1. Set the expressions for [tex]\( y \)[/tex] equal:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]

This results in the equation:

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

Therefore, the equation that can be solved using this system of equations is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]

This matches one of the options given in the problem:
- [tex]\(3x^3 - 7x^2 + 5=7x^4+2x\)[/tex]

This is the equation that can be derived from the given system of equations, and it aligns with the choice provided.