It appears that all you've done is add a constant to X - i.e. X "original" + constant = X "new". This is why only the intercept term changes and not the slope coefficient. That is, you have neither changed the correlation nor the standard deviations - and thus you will not change the slope coefficient.
So, the X's will be perfectly correlated. As a result, when you regress Y on X "original" and X "new" the algorthim will automatically "throw out" X "new" because you have the untenable situation of perfect collinearity.