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Answer :
To solve the problem of matching an equation to the given system of equations, we need to understand what each equation in the provided options represents.
We're given the system of equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
The goal is to find an equation where these two expressions for [tex]\( y \)[/tex] are equal because, in solving the system, we want the outputs (which are both [tex]\( y \)[/tex]) from each expression to be the same for the same [tex]\( x \)[/tex].
So, to find where these equations are equal, we set them equal to each other:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This gives us the equation:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Let's match this with one of the options provided. The correct equation from the options that matches the expression we've derived is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Thus, the correct equation that can be solved using this system of equations is:
[tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
We're given the system of equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
The goal is to find an equation where these two expressions for [tex]\( y \)[/tex] are equal because, in solving the system, we want the outputs (which are both [tex]\( y \)[/tex]) from each expression to be the same for the same [tex]\( x \)[/tex].
So, to find where these equations are equal, we set them equal to each other:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This gives us the equation:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Let's match this with one of the options provided. The correct equation from the options that matches the expression we've derived is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Thus, the correct equation that can be solved using this system of equations is:
[tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
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