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 using the given system of equations, let's analyze the system:

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

Since both expressions are equal to [tex]\( y \)[/tex], we can set the right-hand sides of these equations equal to each other to find the relationship between them. This gives us:

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

This equation represents the condition where both expressions for [tex]\( y \)[/tex] are equal. Thus, this is the equation that can be solved using the system of equations provided.

In summary, the equation that can be solved with the given system is:

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