Answer :
To determine which equation can be solved using the given system of equations, let's take a closer look at the system provided:
The system consists of two equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find an equation that can be solved, we need to identify when these two expressions for [tex]\( y \)[/tex] are equal, which means setting the right-hand sides equal to each other:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This is the equation you get when solving this system by equating the two expressions for [tex]\( y \)[/tex].
We can also rearrange this equation by bringing all terms to one side to simplify or solve it further. So, subtract the entire right side [tex]\( 7x^4 + 2x \)[/tex] from both sides:
[tex]\[ 3x^3 - 7x^2 + 5 - (7x^4 + 2x) = 0 \][/tex]
Simplifying, we get:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x - 5 = 0 \][/tex]
Therefore, the equation you can solve using the system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
or in its rearranged form:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x - 5 = 0 \][/tex]
These equations involve equating and manipulating the system equations provided.
The system consists of two equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find an equation that can be solved, we need to identify when these two expressions for [tex]\( y \)[/tex] are equal, which means setting the right-hand sides equal to each other:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This is the equation you get when solving this system by equating the two expressions for [tex]\( y \)[/tex].
We can also rearrange this equation by bringing all terms to one side to simplify or solve it further. So, subtract the entire right side [tex]\( 7x^4 + 2x \)[/tex] from both sides:
[tex]\[ 3x^3 - 7x^2 + 5 - (7x^4 + 2x) = 0 \][/tex]
Simplifying, we get:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x - 5 = 0 \][/tex]
Therefore, the equation you can solve using the system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
or in its rearranged form:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x - 5 = 0 \][/tex]
These equations involve equating and manipulating the system equations provided.
