Answer :
To solve the problem of finding which equation can be solved using the given system of equations, we have the following two equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To determine which equation can be solved using this system, let's set the two expressions for [tex]\( y \)[/tex] equal to each other because they both equal [tex]\( y \)[/tex]:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Next, let's rearrange this equation so that all terms are on one side, with zero on the other side. This involves moving all terms from one side to the other:
[tex]\[ 0 = 7x^4 + 2x - 3x^3 + 7x^2 - 5 \][/tex]
Or equivalently:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \][/tex]
This rearranged equation represents the equation that can be solved using the given system of equations. Therefore, the correct choice is:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \][/tex]
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To determine which equation can be solved using this system, let's set the two expressions for [tex]\( y \)[/tex] equal to each other because they both equal [tex]\( y \)[/tex]:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Next, let's rearrange this equation so that all terms are on one side, with zero on the other side. This involves moving all terms from one side to the other:
[tex]\[ 0 = 7x^4 + 2x - 3x^3 + 7x^2 - 5 \][/tex]
Or equivalently:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \][/tex]
This rearranged equation represents the equation that can be solved using the given system of equations. Therefore, the correct choice is:
[tex]\[ 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \][/tex]
