Response of LTI System A to x(t): y(t)=x(t)-x(t-2a)

[peripatein]

Hi,
y(t) is the response of LTI system A to x(t). How could I have figured out that y(t) = x(t) - x(t-2a) (please see attachment). By looking at the graphs this isn't apparent to me :S.

 

[smk037]

Write out the equations of the lines. You know that the equations are equal for 0<t<2a and 4a<t<6a.

Write out the equation of y(t) for 2a<t<4a. Relate that equation to the equation for x(t).

 

[peripatein]

x(t) = 2t - 2(t-a) + 2(t-3a) - 2(t-4a)
y(t) = 2t - 2(t-a) - 4(t-2a) + 4(t-3a) + 2(t-4a) - 2(t-5a) + 2(t-6a)
These are the equations of the lines. Would you agree?