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Answer :
To solve this question, we need to determine which equation can be derived from the given system of equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find an equation from this system, we set the two expressions for [tex]\( y \)[/tex] equal to each other because they both describe the same [tex]\( y \)[/tex] value:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This is the equation we get from solving for when both expressions for [tex]\( y \)[/tex] are equal. Comparing it with the option choices:
1. [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
2. [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
3. [tex]\( 7x^4 + 2x = 0 \)[/tex]
4. [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
The correct equation derived from setting the two equations for [tex]\( y \)[/tex] equal is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Thus, option 2 is the one that can be solved using this system of equations.
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find an equation from this system, we set the two expressions for [tex]\( y \)[/tex] equal to each other because they both describe the same [tex]\( y \)[/tex] value:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This is the equation we get from solving for when both expressions for [tex]\( y \)[/tex] are equal. Comparing it with the option choices:
1. [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
2. [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
3. [tex]\( 7x^4 + 2x = 0 \)[/tex]
4. [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
The correct equation derived from setting the two equations for [tex]\( y \)[/tex] equal is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Thus, option 2 is the one that can be solved using this system of equations.
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