Answer :
To solve this question, we need to identify which equation from the given options can be derived using the two equations in the provided system of equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
We're looking for an equation that can be solved using this system. Typically, when faced with two equations that both equal [tex]\( y \)[/tex], we can equate them to find a possible solution.
Here’s the step-by-step breakdown:
1. Identify the System of Equations:
- We have the equations:
[tex]\[
y = 3x^3 - 7x^2 + 5
\][/tex]
[tex]\[
y = 7x^4 + 2x
\][/tex]
2. Set the Expressions for [tex]\( y \)[/tex] Equal to Each Other:
- Since both expressions are equal to [tex]\( y \)[/tex], we equate them:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
3. Find the Corresponding Option:
- Check which of the given options matches this equation:
- [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]
- The equation [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex] matches with the second option.
Therefore, the equation that can be solved using the provided system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This option corresponds to the second choice in the list.
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
We're looking for an equation that can be solved using this system. Typically, when faced with two equations that both equal [tex]\( y \)[/tex], we can equate them to find a possible solution.
Here’s the step-by-step breakdown:
1. Identify the System of Equations:
- We have the equations:
[tex]\[
y = 3x^3 - 7x^2 + 5
\][/tex]
[tex]\[
y = 7x^4 + 2x
\][/tex]
2. Set the Expressions for [tex]\( y \)[/tex] Equal to Each Other:
- Since both expressions are equal to [tex]\( y \)[/tex], we equate them:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
3. Find the Corresponding Option:
- Check which of the given options matches this equation:
- [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]
- The equation [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex] matches with the second option.
Therefore, the equation that can be solved using the provided system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This option corresponds to the second choice in the list.
