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Answer :
Sure, let's determine which equation can be solved using the given system of equations:
The system of equations is:
[tex]\[
\left\{\begin{array}{l}
y = 3x^3 - 7x^2 + 5 \\
y = 7x^4 + 2x
\end{array}\right.
\][/tex]
To find the equation that can be solved using this system, we need to consider the equations given in the choices:
1. [tex]\(3x^3 - 7x^2 + 5 = 0\)[/tex]
2. [tex]\(3x^3 - 7x^2 + 5 = 7x^4 + 2x\)[/tex]
3. [tex]\(7x^4 + 2x = 0\)[/tex]
4. [tex]\(7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0\)[/tex]
For the correct equation, we need one that aligns with the system of equations given. The system provides two expressions for [tex]\(y\)[/tex]:
1. [tex]\(y = 3x^3 - 7x^2 + 5\)[/tex]
2. [tex]\(y = 7x^4 + 2x\)[/tex]
If we set these two expressions for [tex]\(y\)[/tex] equal to each other, we get:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This equation is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
So, the correct equation that can be solved using the given system is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
Thus, the answer is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
The system of equations is:
[tex]\[
\left\{\begin{array}{l}
y = 3x^3 - 7x^2 + 5 \\
y = 7x^4 + 2x
\end{array}\right.
\][/tex]
To find the equation that can be solved using this system, we need to consider the equations given in the choices:
1. [tex]\(3x^3 - 7x^2 + 5 = 0\)[/tex]
2. [tex]\(3x^3 - 7x^2 + 5 = 7x^4 + 2x\)[/tex]
3. [tex]\(7x^4 + 2x = 0\)[/tex]
4. [tex]\(7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0\)[/tex]
For the correct equation, we need one that aligns with the system of equations given. The system provides two expressions for [tex]\(y\)[/tex]:
1. [tex]\(y = 3x^3 - 7x^2 + 5\)[/tex]
2. [tex]\(y = 7x^4 + 2x\)[/tex]
If we set these two expressions for [tex]\(y\)[/tex] equal to each other, we get:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This equation is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
So, the correct equation that can be solved using the given system is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
Thus, the answer is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
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