Yes, it's pretty common, and it usually goes "You can't have your cake and eat it too." Some people tend to put a comma after the word it, but it commonly appears both ways.Is the following proverb a popular one in English?
you canít have your cake, and eat it?
And I would also like to know here if the sentence is similar to " There is a necessary trade-off between ... and..."
The idea of there being a necessary trade-off between two things sounds about right as far as the meaning is concerned. In other words, you can't always have everything go your way. Most situations involve some give and take. You have to give up something to get something. For example:
Sue: You know Jane, since I went back to work full-time, I just haven't been able to spend as much time with my kids as I would like.
Jane: I know what you mean. After all, there are only twenty-four hours in a day. I guess you can't have your cake and eat it too.
Student or Learner