How do I not make children cry

I had my first math lesson with a 9-th grade child today. I asked her to show me some problems she struggled with. She gave me her homework assignment problem. I asked her questions to assess where she's at: how would you approach this problem, do you know Pythagoras theorem, do you know what a square is, until we found she doesn't know how much is 5×5. She can add and multiply 4x4 though. Her mother was there the whole time and sometimes answered questions directed at the child. 🧐

The child grew increasingly distressed and I tried to reassure her to not be embarrassed, that I just need to understand where she's currently at, but I obviously didn't do a very good job. The mother at this point brought up that she hoped we could solve the whole homework together in an hour. I explained that I could either solve the homework out loud myself while the child understands nothing, or I could properly explain things, but it could not be done in an hour. Then I agreed to try and walk her through the homework quickly but I still tried to at least explain the gist to her and check that she understands at least some part of the solution, and at that point she was on the verge of tears.

I stopped at this point and asked the child if getting the homework done was really the highest priority. I suggested accepting the L on this homework and focusing on teaching the basics, instead of me basically doing the child's homework out loud while she doesn't understand and cries. The mother was receptive to that and suggested booking another lesson this week so we can work through the homework at a slower pace and actually hopefully learn something.

After we were done with the first problem (out of 4), I spent the last 5 minutes just chatting to her and trying to make her feel better, but she was shy and upset and barely talked. I feel I should've handled this differently, maybe refused the solving homework thing outright. What can I do to make the student feel more at ease? How can I help her handle homework in a reasonable time without just solving it for her, when she's missing so much basic knowledge?