Reduce System of 3 ODEs to 2 ODEs

Question

I'm currently self-studying the book "Nonlinear Dynamics and Chaos". I got the following system

$$ \dot{x} = -kxy \\ \dot{y} = kxy - ly \\ \dot{z} = ly $$

According to a comment on one of Strogatzs' videos on Youtube one is able to reduce this system to 2 equations. I never did something along the lines so I'm not quite sure how to do this. $\dot{y}$ looks like a combination of the other two. Can I simply say something along the lines that $\dot{y}$ is equal to $-(\dot{x} - \dot{z})$ and simply apply the methods I already know to to $\dot{x}$ and $\dot{z}$?

In the book is an exercise where they combine the system to a single ODE, but I don't really get how as well. I assume combining it to two ODEs must be simpler.

I would appreciate some help or some resource I can check out to understand the process better.

Answer 1

$$\dot{x} = -kxy \\ \dot{y} = kxy - ly \\ \dot{z} = ly$$ Add all the DE: $$\dfrac {d}{dt}(x+y+z)=0$$ $$x+y+z=C$$

Answer 2

I would solve the 2 first equations for $x,y,$ and then $z=-x-y+C.$