Answer:
{(x,y,z) : x = 1 - s - , y = s, z = t, s, t ∈ R}
Step-by-step explanation:
We will rearrange the linear equation for x + y + z = 1 that is
x + y + z = 1
x = 1 - y - z
Here there are three variables and one equation. So, there will be two parameters.
Let us assume parameters of s and t for free variables that is
y = s and
z = t
which lies
x = 1 - s - t
Therefore, the parametric representation will be
x = 1 - s - t
y = s
z = t
So, the answer set of the linear equation x + y + z = 1 is
{(x,y,z) : x = 1 - s - , y = s, z = t, s, t ∈ R}
