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Answer :
To find which equation can be solved using the given system of equations:
1. Understand the System of Equations:
We have a system of two equations:
- [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
- [tex]\( y = 7x^4 + 2x \)[/tex]
2. Identify the Method to Combine Equations:
Since both equations equal [tex]\( y \)[/tex], we can set them equal to each other to find a relationship involving only [tex]\( x \)[/tex].
3. Set the Equations Equal:
By substituting [tex]\( y \)[/tex] from the first equation into the second, or vice-versa, we equate the two expressions:
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
4. Recognize the Resulting Equation:
The equation [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex] can be solved for [tex]\( x \)[/tex], as it originated by equating the two expressions given by the system.
Based on these steps, the equation that can be solved using the given system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
1. Understand the System of Equations:
We have a system of two equations:
- [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
- [tex]\( y = 7x^4 + 2x \)[/tex]
2. Identify the Method to Combine Equations:
Since both equations equal [tex]\( y \)[/tex], we can set them equal to each other to find a relationship involving only [tex]\( x \)[/tex].
3. Set the Equations Equal:
By substituting [tex]\( y \)[/tex] from the first equation into the second, or vice-versa, we equate the two expressions:
- [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
4. Recognize the Resulting Equation:
The equation [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex] can be solved for [tex]\( x \)[/tex], as it originated by equating the two expressions given by the system.
Based on these steps, the equation that can be solved using the given system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
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