College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Which equation can be solved by using this system of equations?

[tex]\[

\begin{array}{l}

y = 3x^3 - 7x^2 + 5 \\

y = 7x^4 + 2x

\end{array}

\][/tex]

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

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

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

D. [tex]\( 7x^4 + 2x = 0 \)[/tex]

Answer :

To solve this problem, we're given two equations and four possible options for which a system of equations can be solved. Let's analyze the equations:

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

To find an equation that can be solved using this system, we need to set the two expressions for [tex]\( y \)[/tex] equal to each other because they both represent the same [tex]\( y \)[/tex]-value:

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

This equation is formed by equating the two given equations, as they both equal [tex]\( y \)[/tex].

Now, let's analyze the options:

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

Option 1 is exactly the equation we derived from setting the two expressions for [tex]\( y \)[/tex] equal to each other:

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

Therefore, the equation that can be solved using the given system is Option 1: [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex].