Answer :
To solve the given system of equations, it involves two expressions for [tex]\( y \)[/tex]:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
The system of equations shows both expressions equal to [tex]\( y \)[/tex]. To find an equation that can emerge from this system, we set the two expressions equal to each other because they both equal [tex]\( y \)[/tex]:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation is obtained by equating the two functions defined for [tex]\( y \)[/tex]. Essentially, this means we are looking at values of [tex]\( x \)[/tex] that satisfy both equations simultaneously, or intersect points of these two functions.
Therefore, the equation that can be solved using this system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation is checked against the given options, and it matches the second option:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
The system of equations shows both expressions equal to [tex]\( y \)[/tex]. To find an equation that can emerge from this system, we set the two expressions equal to each other because they both equal [tex]\( y \)[/tex]:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation is obtained by equating the two functions defined for [tex]\( y \)[/tex]. Essentially, this means we are looking at values of [tex]\( x \)[/tex] that satisfy both equations simultaneously, or intersect points of these two functions.
Therefore, the equation that can be solved using this system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation is checked against the given options, and it matches the second option:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
