Guessing DSP system characteristics

[kanna]

Samples for guessing a dsp system characteristic given input and output
sequences, like

x_1 = {-1,2 *,1} -> y_1 = {1,2 *,-1,0,1}
x_2 = {1,-1 *,-1} -> y_2 = {-1,1 *,0,2}
x_3 = {0,1 *,1} -> y_3{1 *,2,1}

* denotes 0 time instant.

I understand x_1 + x_2 is the impulse. How to proceed after that?

Thanks