Tutoring English, you deal with these issues constantly.  In this post, the English tutor sheds light on a couple of common sentence faults.

You burnt the cake she is furious.      fused sentence

You burnt the cake, she is furious.     comma splice

Neither the fused sentence nor the comma splice is correct.  Both are found commonly in everyday writing.  The comma splice is even found in published writing.

The problem with both the fused sentence and the comma splice is that each produces a run-on sentence. A run-on sentence is incorrect.  A simple way to identify one is that its subject changes or is restated without a semicolon or conjunction in between. There are other punctuation fixes besides the semicolon, but a comma by itself won’t work.

You burnt the cake she is furious.           Subject change from you to she.
I went to Bill’s party, I had a great time.    I is restated.

Facing a fused sentence or a comma splice, the same fixes can be used.  One solution is to add a conjunction before the second subject; another is to use a semicolon.

Fused sentences and comma splices are best gotten rid of. Changing habits always seems easier at the beginning of the school year:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Source: Harbrace Handbook for Canadians, sixth edition. 2003: Nelson Education Ltd.