systems of equations with exponents?

Question

I am building a website which will run on the equation specified below. I am in pre-algebra and do not have any idea how to go about this equation. my friends say it is a system of equation but I don't know how to solve those and no one I know seems to know how to do them with exponents. I was hoping that people on this site could tell me the answer to the problem. if you could explain how to do it not for me but for people in my situation with more experience that might make the question better for everyone ells looking into it. Thank you for your answer!

Here is the system of equations:

$xy^5=8000$

$(xy^4)-(xy^3)=5000$

Answer 1

The first equation tells you that $x=\frac{8000}{y^5}$. Substituting that into the second equation you have $\frac{8000}{y^5}y^4-\frac{8000}{y^5}y^3=5000$ $$\frac{8000}{y}-\frac{8000}{y^2}=5000\\\frac{y^2}{1000}(\frac{8000}{y}-\frac{8000}{y^2}=5000)\\8y-8=5y^2\\5y^2-8y+8=0$$

But that gives imaginary roots, so either they never intersect or I did something wrong... Lemme check.

Answer 2

Multiply second equation with $y^2$ then you get

$$xy^5 \cdot y-xy^5=5000y^2$$

Substitute $xy^5=8000$

$$8000y-8000=5000y^2$$

Divide with $1000$ and move all terms to left side

$$5y^2-8y+8=0$$

Since $d=b^2-4ac=(-8)^2-4\cdot5\cdot8=-96$ which is negative, there are no solutions.