Answer :
To identify which equation can be solved using the given system of equations, let's go through the process step-by-step:
1. Understand the System of Equations:
- We have a system of two equations:
[tex]\[
\left\{\begin{array}{l}
y = 3x^3 - 7x^2 + 5 \\
y = 7x^4 + 2x
\end{array}\right.
\][/tex]
2. Set the Equations Equal to Each Other:
- Since both expressions are equal to [tex]\( y \)[/tex], we can set them equal to each other:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
3. Rearrange the Equation:
- To form a single equation, we move all terms to one side of the equation:
[tex]\[
7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0
\][/tex]
- This equation is derived by subtracting the left side from the right side, ensuring that all terms are on one side and the equation is set to zero.
4. Conclusion:
- The equation that can be solved using the given system of equations is:
[tex]\[
7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0
\][/tex]
This step-by-step approach shows how we use the system of equations to derive the single equation that can be solved for [tex]\( x \)[/tex].
1. Understand the System of Equations:
- We have a system of two equations:
[tex]\[
\left\{\begin{array}{l}
y = 3x^3 - 7x^2 + 5 \\
y = 7x^4 + 2x
\end{array}\right.
\][/tex]
2. Set the Equations Equal to Each Other:
- Since both expressions are equal to [tex]\( y \)[/tex], we can set them equal to each other:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
3. Rearrange the Equation:
- To form a single equation, we move all terms to one side of the equation:
[tex]\[
7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0
\][/tex]
- This equation is derived by subtracting the left side from the right side, ensuring that all terms are on one side and the equation is set to zero.
4. Conclusion:
- The equation that can be solved using the given system of equations is:
[tex]\[
7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0
\][/tex]
This step-by-step approach shows how we use the system of equations to derive the single equation that can be solved for [tex]\( x \)[/tex].
