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Answer :
To determine which equation can be solved using the given system of equations, let's look closely at the system:
1. First equation: [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. Second equation: [tex]\( y = 7x^4 + 2x \)[/tex]
Since both equations equal [tex]\( y \)[/tex], we can set these two expressions equal to each other to find a relationship between them. This leads to the equation:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation matches one of the options provided:
- [tex]\( 3 x^3-7 x^2+5=0 \)[/tex]
- [tex]\( 3 x^3-7 x^2+5=7 x^4+2 x \)[/tex]
- [tex]\( 7 x^4+2 x=0 \)[/tex]
- [tex]\( 7 x^4+3 x^3-7 x^2+2 x+5=0 \)[/tex]
The equation [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex] corresponds to the second option. This is the equation derived directly from equating the two given functions, meaning it can indeed be solved using the system of equations.
1. First equation: [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. Second equation: [tex]\( y = 7x^4 + 2x \)[/tex]
Since both equations equal [tex]\( y \)[/tex], we can set these two expressions equal to each other to find a relationship between them. This leads to the equation:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
This equation matches one of the options provided:
- [tex]\( 3 x^3-7 x^2+5=0 \)[/tex]
- [tex]\( 3 x^3-7 x^2+5=7 x^4+2 x \)[/tex]
- [tex]\( 7 x^4+2 x=0 \)[/tex]
- [tex]\( 7 x^4+3 x^3-7 x^2+2 x+5=0 \)[/tex]
The equation [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex] corresponds to the second option. This is the equation derived directly from equating the two given functions, meaning it can indeed be solved using the system of equations.
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