To represent the solution set of a linear equation parametrically, we introduce other parameters like s and t for the free variables.
Every linear equation has n - 1 free variables where n is the number of the variables.
For x + y + z = 2, we have 3 variables and 3 - 1 = 2 free variables.
First, let y and z be the free variables, we first solve the linear equation for x to get:
x = 2 - y - z
Therefore, the parametric representation of the solution set is given by:
x = 2 - s - t
y = s
z = t.
