Answer :
To solve this problem, we're given two equations and four possible options for which a system of equations can be solved. Let's analyze the equations:
1. The given system of equations is:
- [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
- [tex]\( y = 7x^4 + 2x \)[/tex]
To find an equation that can be solved using this system, we need to set the two expressions for [tex]\( y \)[/tex] equal to each other because they both represent the same [tex]\( y \)[/tex]-value:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation is formed by equating the two given equations, as they both equal [tex]\( y \)[/tex].
Now, let's analyze the options:
1. [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
2. [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
3. [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
4. [tex]\( 7x^4 + 2x = 0 \)[/tex]
Option 1 is exactly the equation we derived from setting the two expressions for [tex]\( y \)[/tex] equal to each other:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Therefore, the equation that can be solved using the given system is Option 1: [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex].
1. The given system of equations is:
- [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
- [tex]\( y = 7x^4 + 2x \)[/tex]
To find an equation that can be solved using this system, we need to set the two expressions for [tex]\( y \)[/tex] equal to each other because they both represent the same [tex]\( y \)[/tex]-value:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation is formed by equating the two given equations, as they both equal [tex]\( y \)[/tex].
Now, let's analyze the options:
1. [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
2. [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
3. [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
4. [tex]\( 7x^4 + 2x = 0 \)[/tex]
Option 1 is exactly the equation we derived from setting the two expressions for [tex]\( y \)[/tex] equal to each other:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Therefore, the equation that can be solved using the given system is Option 1: [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex].
