Answer :
To determine which equation can be solved using the given system of equations, let's analyze the system step-by-step:
The system of equations is given as:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find an equation from these that can be solved, we need to equate the two expressions that are set equal to [tex]\( y \)[/tex]. Since both are equal to [tex]\( y \)[/tex], they are equal to each other:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation corresponds to one of the options in the question:
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
Let's now compare this with the provided options:
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 answer is option (2):
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This is the equation obtained by setting the two expressions for [tex]\( y \)[/tex] equal to each other in the system of equations given.
The system of equations is given as:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find an equation from these that can be solved, we need to equate the two expressions that are set equal to [tex]\( y \)[/tex]. Since both are equal to [tex]\( y \)[/tex], they are equal to each other:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation corresponds to one of the options in the question:
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
Let's now compare this with the provided options:
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 answer is option (2):
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This is the equation obtained by setting the two expressions for [tex]\( y \)[/tex] equal to each other in the system of equations given.
