Answer :
To solve this problem, 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]
The question asks us to identify which equation among the given options can be solved using this system of equations.
Since both equations are set equal to [tex]\( y \)[/tex], we can find where these two expressions for [tex]\( y \)[/tex] are equal. This means we set the two expressions equal to each other:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Now, we need to rearrange the terms to bring all terms to one side of the equation, setting the equation to zero:
[tex]\[ 0 = 7x^4 + 2x - 3x^3 + 7x^2 - 5 \][/tex]
Or, equivalently:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \][/tex]
This equation, [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex], corresponds to one of the provided options. Therefore, the correct answer is:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \][/tex]
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
The question asks us to identify which equation among the given options can be solved using this system of equations.
Since both equations are set equal to [tex]\( y \)[/tex], we can find where these two expressions for [tex]\( y \)[/tex] are equal. This means we set the two expressions equal to each other:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Now, we need to rearrange the terms to bring all terms to one side of the equation, setting the equation to zero:
[tex]\[ 0 = 7x^4 + 2x - 3x^3 + 7x^2 - 5 \][/tex]
Or, equivalently:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \][/tex]
This equation, [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex], corresponds to one of the provided options. Therefore, the correct answer is:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \][/tex]
