X axis allignment of two signals with slight delay in time

I am plotting two signals which have slight time delay. I want to make them exact same. I tried make it by subtracting they look alligned but then subtracted signal does not start from 0. The both plots are attached. Is there any possible way to make them align and both start and end at same point.

[KALYAN ACHARJYA]

Have Both Plots resulted(y-axis value) from different equations? You can consider the same x-axis, but y value may vary, clarify?

[Husnain Ahmed]

Actually this data has been plotted from one sensor but data was collected in Real Time PC and another PC that is why there is some difference in the y axis values.

[Aquatris]

Why do you expect the time to start at zero since you shift the signal?

You can either not show the negative time part of the plot by xlim([0 80]) command or instead of doing t = t-delay, do

index = find(t=<delay);
t(delay) =[];
data(delay) = [];
t = t-t(1); % make the time start at 0