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min x if y = x - 2003, z = 2y - 2003, w = 3z - 2003 ofr x,y,z,ww>=0

Source: 2003 Swedish Mathematical Competition p1

March 21, 2021
algebraminsystem of equationsSysteminequalities

Problem Statement

If x,y,z,wx, y, z, w are nonnegative real numbers satisfying {y=x−2003z=2y−2003w=3z−2003\left\{ \begin{array}{l}y = x - 2003 \\ z = 2y - 2003 \\ w = 3z - 2003 \\ \end{array} \right. find the smallest possible value of xx and the values of y,z,wy, z, w corresponding to it.
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