Solve this system of equations.
y = x^(3/2)
y = e^(-x)
My Answer is x = e^(-2x/3).
Is this right?
Nah. The solution to this system is in terms of the Lambert W function which I'd be surprised if you've been taught about.
Lambert W function - Wikipedia, the free encyclopedia
$x=\dfrac 3 2 W(\frac 2 3)$
You sure you have the problem correctly written?
Part of your answer will be the values of x which satisfy this equation. The only way to do that (unless you know the Lambert W Function) is using numerical methods or getting a decimal approximation with a calculator (which also uses numerical methods).
You then need to get the corresponding y values.