A couple of days ago our toilet stopped working. It would not flush.
Yet when we let the water from the bath go down the drain the water from the toilet would decend. The water raises in the toilet when we first start to let the water from the bath drain but when the bath tub is finished draining the toilet water decends. What could cause this?

A clog in the sewer line.

Many years ago I lived in a small house in Prescott AZ. The house was one of the original houses there and was well over 100 years old. Every time I took a bath the toilet could not be flushed as it would overflow. When the bath water finally went down and I waited for at least an hour I could then flush the toilet without it overflowing. Called out the local RotoRooter guy. He cleaned the line all the way from the house to the street to find the clog. He said he would come out on a regular basis every so many years and would find a clog at the same spot each time. The line being 100 years old had something to do with it as well as the new medical facility on the other side of the street that was hooked into the same sewer line as I was that finally went out to the street.

In your case, you just need to find the clog and get rid of it.