By definition, systematic error is an error having constant direction and magnitude in all readings. Consider a situation where your stopwatch starts from 0:00:10 s only; all your readings will have an additive 0.1 s. It will not vary with situations. Such an error can be eliminated by taking a difference/gradient. Consider you had to measure the time interval for a ball to fall between a distance XY; the first reading (when it crossed X) was 0:02:00 s, and the second reading (when it crossed Y) was 0:04:10 s. The time interval is the difference of the two:
4.10 - 2.00 = 2.10.
Even if the systematic error was absent, the DIFFERENCE would be the same i.e. 4.00 - 1.90 = 2.10 s.
Systematic errors do not affect the precision of a measurement, but they affect the accuracy.
By definition, random error is an error having a varying direction and magnitude in all readings. This is quite simple, for instance, given the same example as above--it is not possible for us to start the stopwatch at the exact moment the ball crosses X, as there is a human reaction error of 0.1 to 0.4 seconds. This error cannot be eliminated with a gradient or difference, because it is not constant. A random error does affect the precision of a measurement, but not its accuracy.