High School

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

Since both equations are equal to [tex]$y$[/tex], we can set the right-hand sides equal to each other. This gives:

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

This is the equation that we need to solve to find the common solutions for [tex]$x$[/tex] (and subsequently for [tex]$y$[/tex]). Therefore, the correct equation corresponding to the system is:

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

Thus, the answer is the equation

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

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