Answer :
To solve the given question, we need to determine which equation can be derived from the given system of equations.
The system of equations provided is:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find which equation can be solved using these equations, we can set the two expressions for [tex]\( y \)[/tex] equal to each other, because they both represent [tex]\( y \)[/tex]. This results in a single equation:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Next, let's compare the possible answer 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 equation we derived from the system, [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex], matches the second option exactly. Therefore, the correct answer is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
So, this is the equation that can be solved using the given system of equations.
The system of equations provided is:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find which equation can be solved using these equations, we can set the two expressions for [tex]\( y \)[/tex] equal to each other, because they both represent [tex]\( y \)[/tex]. This results in a single equation:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Next, let's compare the possible answer 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 equation we derived from the system, [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex], matches the second option exactly. Therefore, the correct answer is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
So, this is the equation that can be solved using the given system of equations.
