Finding equilibria of several ODEs I am trying to find the equilibria (w.r.t variables $a$, $b$, $c$, $e$ & $f$) of the following ODEs:
$$\frac{dx}{dt} = a + x(1-x)-xz - bx$$
$$\frac{dy}{dt} = xz - cy$$
$$\frac{dz}{dt} = ey - fz$$
Now I understand I need to set all three ODEs to $0$ and then solve.
So far I have calculated
$z = \frac{ey}{f}$
from $\frac{dz}{dt} = 0$ and then subbing this into $\frac{dy}{dt}$ I get $$\frac{exy}{f} - cy = 0$$
I am unsure where to go from here.

This is an exercise in solving a nonlinear system of equations. Use equation 3 to get $y$ in terms of $z$. Plug that in equation 2 and solve for $z$ in terms of $x$. Then plug that in equation 1. After multiplying out the denominator you should have a cubic polynomial; that can be solved exactly, thought it's tedious.
