Answer :
To solve the problem, we need to determine which equation from the list can be obtained by using the given system of equations. Let's walk through the process step-by-step:
We are given the system of equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find a relationship between these equations, we can set them equal to each other because they both represent [tex]\( y \)[/tex]:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
The goal is to rearrange this into one of the given equation options. Let's move all terms to one side of the equation to see if it matches any of the provided options:
[tex]\[ 3x^3 - 7x^2 + 5 - 7x^4 - 2x = 0 \][/tex]
Now, let's rearrange the terms:
[tex]\[ 7x^4 - 3x^3 + 7x^2 - 2x - 5 = 0 \][/tex]
As we can see, this matches exactly with the equation provided as:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \][/tex]
The correct option is:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \][/tex]
Therefore, the equation from the list that can be solved by using the given system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
We are given the system of equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find a relationship between these equations, we can set them equal to each other because they both represent [tex]\( y \)[/tex]:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
The goal is to rearrange this into one of the given equation options. Let's move all terms to one side of the equation to see if it matches any of the provided options:
[tex]\[ 3x^3 - 7x^2 + 5 - 7x^4 - 2x = 0 \][/tex]
Now, let's rearrange the terms:
[tex]\[ 7x^4 - 3x^3 + 7x^2 - 2x - 5 = 0 \][/tex]
As we can see, this matches exactly with the equation provided as:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \][/tex]
The correct option is:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \][/tex]
Therefore, the equation from the list that can be solved by using the given system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
