Answer :
To determine which equation can be solved using the given system of equations, we need to analyze and compare the equations:
The system of equations given is:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find a common equation from the given choices, let's follow these steps:
1. Set the two expressions for [tex]\( y \)[/tex] equal to each other:
Since both equations define [tex]\( y \)[/tex], we can set them equal to each other for comparison:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This equation directly matches one of the options provided:
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
2. Express the equation in a standard polynomial form:
- Rearrange the equation by moving all terms to one side:
[tex]\[
0 = 7x^4 + 3x^3 - 7x^2 + 2x + 5
\][/tex]
This re-arranged equation also matches one of the provided options:
- [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
Therefore, both of these equations can be derived from the given system of equations:
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
- [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
These are the equations that can be solved using the given system.
The system of equations given is:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find a common equation from the given choices, let's follow these steps:
1. Set the two expressions for [tex]\( y \)[/tex] equal to each other:
Since both equations define [tex]\( y \)[/tex], we can set them equal to each other for comparison:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This equation directly matches one of the options provided:
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
2. Express the equation in a standard polynomial form:
- Rearrange the equation by moving all terms to one side:
[tex]\[
0 = 7x^4 + 3x^3 - 7x^2 + 2x + 5
\][/tex]
This re-arranged equation also matches one of the provided options:
- [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
Therefore, both of these equations can be derived from the given system of equations:
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
- [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
These are the equations that can be solved using the given system.
