Answer :
To determine which equation can be solved using the given system of equations, let's carefully analyze and compare the system:
1. The system provided is:
- Equation 1: [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
- Equation 2: [tex]\( y = 7x^4 + 2x \)[/tex]
2. We want to find out which of the given options can be derived from this system of equations. The choices are:
- [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
- [tex]\( 7x^4 + 2x = 0 \)[/tex]
- [tex]\( 7x^4 + 3x^3 - \sqrt{3}x^2 + 2x + 5 = 0 \)[/tex]
3. Since both equations in the system are equal to [tex]\( y \)[/tex], we can equate them to find a common equation:
- Solution: Set the two expressions for [tex]\( y \)[/tex] equal to each other.
- This means [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex].
4. By equating:
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
5. This matches the second option from the choices given.
Thus, the equation that can be solved using this system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
1. The system provided is:
- Equation 1: [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
- Equation 2: [tex]\( y = 7x^4 + 2x \)[/tex]
2. We want to find out which of the given options can be derived from this system of equations. The choices are:
- [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
- [tex]\( 7x^4 + 2x = 0 \)[/tex]
- [tex]\( 7x^4 + 3x^3 - \sqrt{3}x^2 + 2x + 5 = 0 \)[/tex]
3. Since both equations in the system are equal to [tex]\( y \)[/tex], we can equate them to find a common equation:
- Solution: Set the two expressions for [tex]\( y \)[/tex] equal to each other.
- This means [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex].
4. By equating:
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
5. This matches the second option from the choices given.
Thus, the equation that can be solved using this system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
