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Answer :
To solve this question, we need to determine which equation can be solved using the provided system of equations:
1. The System of Equations:
- [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
- [tex]\( y = 7x^4 + 2x \)[/tex]
2. Understanding the System:
Both equations are expressions for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]. To find a common solution for this system, we need to set these two expressions for [tex]\( y \)[/tex] equal to each other since they both represent the same variable:
[tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
3. Which Equation Solves the System?:
The equation [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex] is the one that directly arises from setting the two expressions equal to each other. Solving this equation will yield the values of [tex]\( x \)[/tex] for which the two expressions for [tex]\( y \)[/tex] will have the same value.
Therefore, the equation we can solve based on this system is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation represents the step necessary to find solutions where both expressions for [tex]\( y \)[/tex] are equal for some values of [tex]\( x \)[/tex].
1. The System of Equations:
- [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
- [tex]\( y = 7x^4 + 2x \)[/tex]
2. Understanding the System:
Both equations are expressions for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]. To find a common solution for this system, we need to set these two expressions for [tex]\( y \)[/tex] equal to each other since they both represent the same variable:
[tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
3. Which Equation Solves the System?:
The equation [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex] is the one that directly arises from setting the two expressions equal to each other. Solving this equation will yield the values of [tex]\( x \)[/tex] for which the two expressions for [tex]\( y \)[/tex] will have the same value.
Therefore, the equation we can solve based on this system is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation represents the step necessary to find solutions where both expressions for [tex]\( y \)[/tex] are equal for some values of [tex]\( x \)[/tex].
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