t= Bx

^{1}+ Dt

^{1}

x= Gx

^{1}+ Ht

^{1}

In the equation for t, why is x being added into the equation? I don't understand, if we are trying to convert time in one reference frame to time in another, why we'd be adding x when x is distance.

Similarly, in the equation for x, why are we adding t?

Also, in the equation for t, I know that the coefficient, D, in front of t

^{1}is γ which is derived from the invariance of the interval. In the equation for, x, though, the authors give vγ (where v is the velocity of the second (rocket) frame from the perspective of the first (earth) frame), as the coefficient of t

^{1}. What is the explanation for that?

Thank you.