If Kyle and Matt never are at the same distance at the same time, the lines described by the system of equations will never cross each other.
We can use the situation where both have the same speed, and Matt drives 50 miles before Kyle starts travelling.
In this case, they're at the same speed, but separated by 50 miles, thus they never will be at the same distance, at the same time.
The system would be:
Since the two lines never touches, the system has no solutions.