Answer :
To find which equation can be solved using the given system of equations, let's break it down step by step:
The system of equations is:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
We want to find the equation that can be solved using these equations. Specifically, we need to find an equation that relates directly to the given system.
### Step-by-Step Solution:
1. Understand the System: Both equations equal [tex]\( y \)[/tex], which means we can set them equal to each other:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
2. Rearrange the Equation: To solve for [tex]\( x \)[/tex], rearrange the equation by bringing all terms to one side:
[tex]\[
0 = 7x^4 - 3x^3 + 7x^2 - 2x - 5
\][/tex]
This equation is formed by subtracting the terms on the right side of the equation from those on the left side.
3. Check the Options: Among the provided options, the equation that matches the form obtained from the system is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
Therefore, the correct equation that can be solved using this system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation arose from setting the two expressions for [tex]\( y \)[/tex] equal and rearranging the terms, which matches the system provided.
The system of equations is:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
We want to find the equation that can be solved using these equations. Specifically, we need to find an equation that relates directly to the given system.
### Step-by-Step Solution:
1. Understand the System: Both equations equal [tex]\( y \)[/tex], which means we can set them equal to each other:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
2. Rearrange the Equation: To solve for [tex]\( x \)[/tex], rearrange the equation by bringing all terms to one side:
[tex]\[
0 = 7x^4 - 3x^3 + 7x^2 - 2x - 5
\][/tex]
This equation is formed by subtracting the terms on the right side of the equation from those on the left side.
3. Check the Options: Among the provided options, the equation that matches the form obtained from the system is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
Therefore, the correct equation that can be solved using this system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation arose from setting the two expressions for [tex]\( y \)[/tex] equal and rearranging the terms, which matches the system provided.
