parametric equation of two equations of one line

Question

Hi I would like to find the parametric equation of the line:

$\ \left\{ x+y=2 , 3x+y+z = 5 \right\} $

I have tried to solve it by posing $z = t $ and it gives me

$\ \left\{ x=-(t-3)/2 , y = (t+1)/2, z =t \right\} $

but I don't know if it is right.

Thank you.

Answer 1

It is correct.

You could also go like this $$\begin{align} x&=t\\ y&=2-t\\ z&=5-(2-t)-3t=3-2t \end{align}$$