Answer :
To solve the problem of identifying which equation can be solved using the given system of equations, follow these steps:
1. Understand the System of Equations:
We have the following system of equations:
[tex]\[
y = 3x^3 - 7x^2 + 5
\][/tex]
[tex]\[
y = 7x^4 + 2x
\][/tex]
2. Equate the Two Expressions for y:
Since both expressions are equal to y, we can set them equal to each other:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
3. Identify the Resulting Equation:
By setting the two equations equal, we've derived an equation that combines both expressions in terms of [tex]\(x\)[/tex]:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
4. Check Against Given Options:
We need to see which of the given options matches the equation we derived:
- [tex]\(3x^3 - 7x^2 + 5 = 0\)[/tex]
- [tex]\(3x^3 - 7x^2 + 5 = 7x^4 + 2x\)[/tex]
- [tex]\(7x^4 + 2x = 0\)[/tex]
- [tex]\(7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0\)[/tex]
The equation we derived, [tex]\(3x^3 - 7x^2 + 5 = 7x^4 + 2x\)[/tex], matches the second option.
Thus, the correct equation that can be solved by using the given system of equations is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
1. Understand the System of Equations:
We have the following system of equations:
[tex]\[
y = 3x^3 - 7x^2 + 5
\][/tex]
[tex]\[
y = 7x^4 + 2x
\][/tex]
2. Equate the Two Expressions for y:
Since both expressions are equal to y, we can set them equal to each other:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
3. Identify the Resulting Equation:
By setting the two equations equal, we've derived an equation that combines both expressions in terms of [tex]\(x\)[/tex]:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
4. Check Against Given Options:
We need to see which of the given options matches the equation we derived:
- [tex]\(3x^3 - 7x^2 + 5 = 0\)[/tex]
- [tex]\(3x^3 - 7x^2 + 5 = 7x^4 + 2x\)[/tex]
- [tex]\(7x^4 + 2x = 0\)[/tex]
- [tex]\(7x^4 + 3x^3 - 7x^2 + 2x + 5 = 0\)[/tex]
The equation we derived, [tex]\(3x^3 - 7x^2 + 5 = 7x^4 + 2x\)[/tex], matches the second option.
Thus, the correct equation that can be solved by using the given system of equations is:
[tex]\[
3x^3 - 7x^2 + 5 = 7x^4 + 2x
\][/tex]
