What to say to a student who has failed? A student has failed a course I just taught. Grades were announced yesterday. This student sent me a very long heartbreaking email about how this means she will be kicked out of her program, how she tried very hard, and how she wants me to reconsider her final grade.

I'm relatively new at being a university instructor; this isn't the first course I've taught at a university, nor is it the first time I've had a student fail a course. But this is the first time I've had a student beg and plead with me, and I'm not sure how to respond. 

I genuinely feel bad for her, as she tried hard and came frequently to my office hours, but I ultimately believe that she did not demonstrate on the final exam that she had a good enough handle on the course material to pass. 

What should I say to politely tell her that she will still fail, without sounding insensitive? 

Edit: Some more relevant information, since some have asked. The course in question is a calculus course for an Engineering program. The student has previously failed and retaken courses, but she is not permitted to have any more failing grades if she wants to remain in the Engineering program. Failing this course is essentially her last `strike'. She will still be allowed to study at the university, but in a different program.

Edit 2: Thanks for all the responses. I wasn't looking for moral justification for failing her or looking for alternative solutions to the situation. I was simply looking for advice on how to respond in a professional manner. And I certainly got that advice from some of the responses.

In the end, I essentially responded with a concise email stating essentially that, while I sympathize with her situation, there was nothing I could do in good conscience to modify her grade at this time, and that I did not believe she demonstrated sufficient mastery of the material to warrant a grade of 50% on the exam. Then I closed with "I wish you the best of luck in your future studies. Sincerely, [me]"

It still doesn't make me feel any better about failing her. :(

(I also will add that this my first time teaching this particular course, and I have certainly learned my own lessons for next time. In particular regarding common misconceptions in the material and what to focus on in the lectures. This will hopefully mitigate the chance of a future student failing in a similar way.)

Edit 3: A few comments have suggested that I might reconsider the student's exam grade. To be clear, this student had about a 50% average in the course going into the final and would have therefore needed at least a 50% on the final exam to pass the course. However, the student only received about 35% on the final (while the average for the class on the final was 73%). I could not, in good conscience, bump the score so significantly to warrant giving out a passing grade in this case. 

It was clear to me that the student had failed. I was only asking for advice on how to respond to her request that I pass her!
I think that you explained the situation very clearly and sensitively in your third paragraph, and that you should send a message to the student along the same lines. All you'd really have to say is that while you of course sympathize with the student, her performance on the final exam makes clear that she did not gain sufficient mastery of the course material to pass the class.

I'll add that I think your message to the student should be clear and concise. The longer your response to the student the more likely it is that you'll wind up in a long, drawn out exchange that stresses both of you out while benefiting no one.