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Answer :
To determine which equation can be solved using the given system of equations, we need to examine what the system tells us and compare it to the provided options:
The system of equations given is:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
Step 1: Analyze the equations.
These two equations are equal to [tex]\( y \)[/tex], so we can set them equal to each other:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This is Option 2 from the list.
Step 2: Examine each option to see which can be derived from the system:
- Option 1: [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
This option is not derived directly from setting the two equations equal to each other, but it comes from setting the first equation [tex]\( 3x^3 - 7x^2 + 5 \)[/tex] equal to zero.
- Option 3: [tex]\( 7x^4 + 2x = 0 \)[/tex]
This option comes from setting the second equation [tex]\( 7x^4 + 2x \)[/tex] equal to zero.
- Option 4: [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
This equation combines terms from both equations by rearranging the expression [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex].
Conclusion:
The equation that is directly derived by setting the two expressions for [tex]\( y \)[/tex] equal to each other is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Thus, the equation that can be solved using this system is Option 2.
The system of equations given is:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
Step 1: Analyze the equations.
These two equations are equal to [tex]\( y \)[/tex], so we can set them equal to each other:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This is Option 2 from the list.
Step 2: Examine each option to see which can be derived from the system:
- Option 1: [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
This option is not derived directly from setting the two equations equal to each other, but it comes from setting the first equation [tex]\( 3x^3 - 7x^2 + 5 \)[/tex] equal to zero.
- Option 3: [tex]\( 7x^4 + 2x = 0 \)[/tex]
This option comes from setting the second equation [tex]\( 7x^4 + 2x \)[/tex] equal to zero.
- Option 4: [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
This equation combines terms from both equations by rearranging the expression [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex].
Conclusion:
The equation that is directly derived by setting the two expressions for [tex]\( y \)[/tex] equal to each other is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Thus, the equation that can be solved using this system is Option 2.
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