Parametric Representation of a Solution Set

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Textbook page for Example 3, Parametric Representation of a Solution Set: solves 3x + 2y - z = 3 by taking y and z as free variables, giving x = 1 - (2/3)s + (1/3)t, y = s, z = t, and two particular solutions.


How did he found x = 1, y = 0, z = 0 and x = 1, y = 1, z = 2?
 
he says that there is a solution for any ##y## and ##z## so he just chose a couple of simple examples. For example ##y=0, \ z=0##.