Find a parametric representation of the solution set of the linear equation. x+y+z=1x+y+z=1

{(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}

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.