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Answer :
To determine which equation can be solved using the given system of equations, let's first examine the system itself:
[tex]\[
\begin{cases}
y = 3x^3 - 7x^2 + 5 \\
y = 7x^4 + 2x
\end{cases}
\][/tex]
In this system, both equations are equal to [tex]\( y \)[/tex]. To find an equation involving just [tex]\( x \)[/tex], we can set the expressions for [tex]\( y \)[/tex] equal to each other. This means we equate the right-hand sides of both equations:
1. From the first equation, we have: [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex].
2. From the second equation, we have: [tex]\( y = 7x^4 + 2x \)[/tex].
Setting these equal gives us the equation:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This is the equation in which both expressions for [tex]\( y \)[/tex] are set equal. Therefore, the equation that can be solved using the given system is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This matches one of the options provided, which is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This is the equation you can derive and solve based on the given system of equations.
[tex]\[
\begin{cases}
y = 3x^3 - 7x^2 + 5 \\
y = 7x^4 + 2x
\end{cases}
\][/tex]
In this system, both equations are equal to [tex]\( y \)[/tex]. To find an equation involving just [tex]\( x \)[/tex], we can set the expressions for [tex]\( y \)[/tex] equal to each other. This means we equate the right-hand sides of both equations:
1. From the first equation, we have: [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex].
2. From the second equation, we have: [tex]\( y = 7x^4 + 2x \)[/tex].
Setting these equal gives us the equation:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This is the equation in which both expressions for [tex]\( y \)[/tex] are set equal. Therefore, the equation that can be solved using the given system is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This matches one of the options provided, which is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This is the equation you can derive and solve based on the given system of equations.
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