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Answer :
To determine which equation can be solved by using the given system of equations, we have:
1. The first equation is [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex].
2. The second equation is [tex]\( y = 7x^4 + 2x \)[/tex].
Since both expressions are equal to [tex]\( y \)[/tex], we can set them equal to each other to find a suitable equation. This strategy helps us identify where both expressions for [tex]\( y \)[/tex] are equal, representing the point(s) of intersection of the two curves.
Let's set the two expressions equal:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This equation, [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex], is what we're looking for because it arises directly from equating the two expressions of [tex]\( y \)[/tex].
Therefore, the equation that can be solved using this system of equations is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
1. The first equation is [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex].
2. The second equation is [tex]\( y = 7x^4 + 2x \)[/tex].
Since both expressions are equal to [tex]\( y \)[/tex], we can set them equal to each other to find a suitable equation. This strategy helps us identify where both expressions for [tex]\( y \)[/tex] are equal, representing the point(s) of intersection of the two curves.
Let's set the two expressions equal:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
This equation, [tex]\( 3x^3 - 7x^2 + 5 = 7x^4 + 2x \)[/tex], is what we're looking for because it arises directly from equating the two expressions of [tex]\( y \)[/tex].
Therefore, the equation that can be solved using this system of equations is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
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