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Answer :
To determine which equation can be solved using the given system of equations, we need to consider each of the equations provided in the context of the system:
The system of equations is:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
The question provides several equations, and we need to identify which one can be solved using the system.
Let's evaluate each option:
1. [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
- This equation solely represents one expression of [tex]\( y \)[/tex] from the first equation in the system. It does not relate to the second equation, so it cannot be solved using the entire system.
2. [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
- This equation involves setting the two expressions for [tex]\( y \)[/tex] equal to each other. It's derived directly from the system by equating the right-hand sides of the two equations. Therefore, this is the equation that can be solved using the system of equations.
3. [tex]\( 7x^4 + 2x = 0 \)[/tex]
- This equation independently represents one expression of [tex]\( y \)[/tex] from the second equation in the system. Like the first option, it does not involve the entire system.
4. [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
- This equation combines and modifies the terms from both expressions for [tex]\( y \)[/tex], but it is not directly derived by a simple operation (like equating) from the two given equations in the system.
After analyzing all options, the correct answer is:
[tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
This equation can be directly solved using the provided system as it equates both expressions for [tex]\( y \)[/tex] from the system of equations.
The system of equations is:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
The question provides several equations, and we need to identify which one can be solved using the system.
Let's evaluate each option:
1. [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
- This equation solely represents one expression of [tex]\( y \)[/tex] from the first equation in the system. It does not relate to the second equation, so it cannot be solved using the entire system.
2. [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
- This equation involves setting the two expressions for [tex]\( y \)[/tex] equal to each other. It's derived directly from the system by equating the right-hand sides of the two equations. Therefore, this is the equation that can be solved using the system of equations.
3. [tex]\( 7x^4 + 2x = 0 \)[/tex]
- This equation independently represents one expression of [tex]\( y \)[/tex] from the second equation in the system. Like the first option, it does not involve the entire system.
4. [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
- This equation combines and modifies the terms from both expressions for [tex]\( y \)[/tex], but it is not directly derived by a simple operation (like equating) from the two given equations in the system.
After analyzing all options, the correct answer is:
[tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
This equation can be directly solved using the provided system as it equates both expressions for [tex]\( y \)[/tex] from the system of equations.
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