Answer :
Certainly! To determine which equation can be solved by using the given system of equations:
1. Understand the System of Equations:
- You are given two equations:
[tex]\[
\begin{align*}
y &= 3x^3 - 7x^2 + 5 \\
y &= 7x^4 + 2x
\end{align*}
\][/tex]
2. Set the Equations Equal to Each Other:
- Since both equations are equal to [tex]\( y \)[/tex], you can set them equal to each other to eliminate [tex]\( y \)[/tex] and find a relationship between [tex]\( x \)[/tex] and itself:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
3. Identify the Equation from the Options:
- Compare the derived equation from setting the two given equations equal to each other ([tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]) with the options provided:
- [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
- [tex]\( 7x^4 + 2x = 0 \)[/tex]
- [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
- You can see that the second option, [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex], matches exactly with the equation we derived from the system.
4. Conclude:
- Therefore, the equation that can be solved using the given system of equations is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This equation represents the relationship between the variables derived from the two expressions in the system when they are set equal to each other.
1. Understand the System of Equations:
- You are given two equations:
[tex]\[
\begin{align*}
y &= 3x^3 - 7x^2 + 5 \\
y &= 7x^4 + 2x
\end{align*}
\][/tex]
2. Set the Equations Equal to Each Other:
- Since both equations are equal to [tex]\( y \)[/tex], you can set them equal to each other to eliminate [tex]\( y \)[/tex] and find a relationship between [tex]\( x \)[/tex] and itself:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
3. Identify the Equation from the Options:
- Compare the derived equation from setting the two given equations equal to each other ([tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]) with the options provided:
- [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
- [tex]\( 7x^4 + 2x = 0 \)[/tex]
- [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
- You can see that the second option, [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex], matches exactly with the equation we derived from the system.
4. Conclude:
- Therefore, the equation that can be solved using the given system of equations is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This equation represents the relationship between the variables derived from the two expressions in the system when they are set equal to each other.
