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Answer :
To determine which equation can be solved using the given system of equations, let's take a closer look at what we have:
We are given a system of equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find a relation between these equations, let's set them equal to each other since they both equal [tex]\( y \)[/tex]:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Now, let's analyze the options given in the question:
1. [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]: This equation is derived from setting the first equation equal to zero, which doesn’t directly solve the system as a whole.
2. [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]: This equation is exactly the one we obtained by equating the two expressions for [tex]\( y \)[/tex]. So this is the equation that directly represents solving the system.
3. [tex]\( 7x^4 + 2x = 0 \)[/tex]: This equation comes from setting just the second equation equal to zero, which is not the goal for solving the system.
4. [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]: This equation appears to rearrange and combine terms in a way that doesn’t match simply equating and solving the given system.
Thus, the equation that can be solved using this system is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
The correct answer is choice 2.
We are given a system of equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find a relation between these equations, let's set them equal to each other since they both equal [tex]\( y \)[/tex]:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Now, let's analyze the options given in the question:
1. [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]: This equation is derived from setting the first equation equal to zero, which doesn’t directly solve the system as a whole.
2. [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]: This equation is exactly the one we obtained by equating the two expressions for [tex]\( y \)[/tex]. So this is the equation that directly represents solving the system.
3. [tex]\( 7x^4 + 2x = 0 \)[/tex]: This equation comes from setting just the second equation equal to zero, which is not the goal for solving the system.
4. [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]: This equation appears to rearrange and combine terms in a way that doesn’t match simply equating and solving the given system.
Thus, the equation that can be solved using this system is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
The correct answer is choice 2.
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