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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.

msm
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Pierre-Luc Bolduc
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    One way to check, since all your equations are linear, is to plug in two (or more) values for $t$, and see whether each corresponding $(x,y,z)$ satisfies the original two equations. Since $t=0$ and $t=1$ give good points, I declare that your solution is good. – Lubin Sep 28 '16 at 00:43

1 Answers1

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It is correct.

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

msm
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  • I found the point P0 (intersection between D1 and D2) but i need to find the parametric equation of a line L passing by P0 and that is perpendicular to the plan with D1 and D2. Do you have any idea how i cound do that? thank you :) – Pierre-Luc Bolduc Sep 28 '16 at 01:02
  • You also need to add $D_2$ equation. Also, you may need to ask a new question... – msm Sep 28 '16 at 01:32