We live on a finite planet with finite resources. What do you do with children if immortality becomes a thing? Should we sterilize people? Kill the young if it

We live on a finite planet with finite resources. What do you do with children if immortality becomes a thing? Should we sterilize people? Kill the young if it gets too much? Or maybe a good old fashioned war between the "old" and young will solve the problem. Look at what's happening in Japan, where the young struggle to get a job because their elders are retiring older and older. Now imagine, they never retire because they are immortal. The only way someone dies is by accident of if someone kills them. How would such a world not devolve into a dystopia?