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Answer :
Certainly! Let's go through the process step-by-step to find which equation can be solved using the given system of equations:
We have a system of equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
Since both expressions are equal to [tex]\( y \)[/tex], we can set them equal to each other to eliminate [tex]\( y \)[/tex]. This gives us the equation:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Now, let's compare this with the options provided:
1. [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
2. [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
3. [tex]\( 7x^4 + 2x = 0 \)[/tex]
4. [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
The equation that we derived by setting the two expressions for [tex]\( y \)[/tex] equal is [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]. This matches exactly with the second option.
Therefore, the equation that can be solved by using this system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
We have a system of equations:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
Since both expressions are equal to [tex]\( y \)[/tex], we can set them equal to each other to eliminate [tex]\( y \)[/tex]. This gives us the equation:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Now, let's compare this with the options provided:
1. [tex]\( 3x^3 - 7x^2 + 5 = 0 \)[/tex]
2. [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]
3. [tex]\( 7x^4 + 2x = 0 \)[/tex]
4. [tex]\( 7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0 \)[/tex]
The equation that we derived by setting the two expressions for [tex]\( y \)[/tex] equal is [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex]. This matches exactly with the second option.
Therefore, the equation that can be solved by using this system of equations is:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
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