### Solve system equations with additional conditions in sage

Hi Sage users,

I've got a system of equations like the following example:

**eq1 = a + b == n * (c + d)** **eq2 = b == k * e**

with n and k must be integers.

for the other variables, there are additional conditions like

**a >= 80** **b >= 1000** **c >= 20** **d >= 40** **a + b <= 2000** **c + d <= 90**

I want to get all solutions of this system where n and k are integers.
Is there a way to find these with sage?

Would be great to get any possible hint to do this!

Thanks for your suggestions,
Tobi