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If so, how should I start?

I know how to derive it while considering 4 scenarios finding values of A, B,D,E in x'=Ax+Bt t'=Dx+Et

and the transformation is:

x'=(x-vt)/sqrt(1-v^2/c^2)

t'=(t-vx/c^2)/sqrt(1-v^2/c^2)

y'=y

z'=z

Thanks beforehand :)