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Answer :
To determine which equation can be solved by using the given system of equations, we need to consider the two equations provided:
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find an equation that can be solved, we should set these two expressions for [tex]\( y \)[/tex] equal to each other. This means we equate their right-hand sides:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation represents one of the options provided. Let's compare this with the listed options:
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]
As we can see, the equation [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex] matches perfectly with option 2, making it the correct choice. This equation is derived by equating the two expressions for [tex]\( y \)[/tex] and represents the system of equations correctly.
1. [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. [tex]\( y = 7x^4 + 2x \)[/tex]
To find an equation that can be solved, we should set these two expressions for [tex]\( y \)[/tex] equal to each other. This means we equate their right-hand sides:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation represents one of the options provided. Let's compare this with the listed options:
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]
As we can see, the equation [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex] matches perfectly with option 2, making it the correct choice. This equation is derived by equating the two expressions for [tex]\( y \)[/tex] and represents the system of equations correctly.
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