Find the end points of a line segment in 3D space

Question

I have a line segment in 3 dimensional space (x,y,z), and I want to find the 2 endpoints of this line segment. Is there a systematic way of doing this?

To be specific, I have the line described by the equations:

$$x+y+z=1$$ $$2y+z=0.5$$ $$x, y, z, \geq 0$$

Here's a picture (I want to find the red line's end points, or parametrize it with $t \in [0,1]$):

Thank you very much!!

Answer 1

You can parametrize your curve with $x$, $y$ or $z$. For the $x$ coordinate you find \begin{equation} x \mapsto \left(x,x - \frac{1}{2} , \frac{3}{2} - 2x \right). \end{equation} Substituting for suitable $x$ gives you the "endpoints".