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Answer :
To determine which equation can be solved using the given system of equations, we need to analyze the two equations in the system:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
We set these two expressions for [tex]\( y \)[/tex] equal to each other to find any common solutions, which means we're equating the right sides of both equations:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This is the equation we're trying to solve.
Now, let's see all the options given in the problem:
- [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]
From our analysis, the equation that accurately represents setting the two [tex]\( y \)[/tex]-expressions equal to each other is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This matches the second option in the list. This equation represents solving the system as a single equation by finding the value of [tex]\( x \)[/tex] where both expressions for [tex]\( y \)[/tex] are equal.
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
We set these two expressions for [tex]\( y \)[/tex] equal to each other to find any common solutions, which means we're equating the right sides of both equations:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This is the equation we're trying to solve.
Now, let's see all the options given in the problem:
- [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]
From our analysis, the equation that accurately represents setting the two [tex]\( y \)[/tex]-expressions equal to each other is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This matches the second option in the list. This equation represents solving the system as a single equation by finding the value of [tex]\( x \)[/tex] where both expressions for [tex]\( y \)[/tex] are equal.
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