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Answer :
To solve the problem of finding which equation can be solved by using the given system of equations, let's look at the system:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
We're asked to determine which equation from the provided options can be derived from this system.
### Explanation
In order to find which equation is derived from the system, we look for the intersection points of the two equations. This means we set the right-hand sides of the given equations equal to each other. This is because both expressions define [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex], and if they express the same [tex]\( y \)[/tex], they must be equal at particular values of [tex]\( x \)[/tex].
1. Set the equations equal to each other:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This gives us the equation option:
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
This equation compares both expressions for [tex]\( y \)[/tex] from the given system, checking where they have the same values, which is essentially finding the intersection points of the curves represented by the system. Therefore, the equation [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex] is the correct one that can be solved using the given system of equations.
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
We're asked to determine which equation from the provided options can be derived from this system.
### Explanation
In order to find which equation is derived from the system, we look for the intersection points of the two equations. This means we set the right-hand sides of the given equations equal to each other. This is because both expressions define [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex], and if they express the same [tex]\( y \)[/tex], they must be equal at particular values of [tex]\( x \)[/tex].
1. Set the equations equal to each other:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This gives us the equation option:
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
This equation compares both expressions for [tex]\( y \)[/tex] from the given system, checking where they have the same values, which is essentially finding the intersection points of the curves represented by the system. Therefore, the equation [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex] is the correct one that can be solved using the given system of equations.
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