Answer :
To solve the problem, we need to identify which equation can be derived from the given system of equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
The goal is to find a relation between these two equations that leads to one of the options provided.
### Steps to Solve:
1. Understand the System of Equations:
- The system gives us two expressions for [tex]\( y \)[/tex].
- Both expressions equal [tex]\( y \)[/tex], so they must be equal to each other.
2. Equate the Two Expressions:
- Since both expressions for [tex]\( y \)[/tex] describe the same variable, we can set them equal:
[tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
3. Identify the Correct Option:
- By setting the two expressions for [tex]\( y \)[/tex] equal, we obtained the equation:
[tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
4. Verify by Checking the Options:
- Let's review the options to see which matches the equation we derived:
- [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 perfectly with one of the provided options.
Thus, the correct equation that can be solved by using this system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
The goal is to find a relation between these two equations that leads to one of the options provided.
### Steps to Solve:
1. Understand the System of Equations:
- The system gives us two expressions for [tex]\( y \)[/tex].
- Both expressions equal [tex]\( y \)[/tex], so they must be equal to each other.
2. Equate the Two Expressions:
- Since both expressions for [tex]\( y \)[/tex] describe the same variable, we can set them equal:
[tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
3. Identify the Correct Option:
- By setting the two expressions for [tex]\( y \)[/tex] equal, we obtained the equation:
[tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
4. Verify by Checking the Options:
- Let's review the options to see which matches the equation we derived:
- [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 perfectly with one of the provided options.
Thus, the correct equation that can be solved by using this system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
