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 solve this question, we need to determine which equation can be derived from the given system of equations:

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

To find an equation from this system, we set the two expressions for [tex]\( y \)[/tex] equal to each other because they both describe the same [tex]\( y \)[/tex] value:

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

This is the equation we get from solving for when both expressions for [tex]\( y \)[/tex] are equal. Comparing it with the option choices:

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

The correct equation derived from setting the two equations for [tex]\( y \)[/tex] equal is:

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

Thus, option 2 is the one that can be solved using this system of equations.