How to convert half plane from parametric to general form?

Question

I have:

$ x=2+5t $

$y=5-t, t\geq 0 $

and I am supposed to convert it to general form. I know how to do it when I have plane, but that is half plane and I have no idea what will change.

Can anyone help me?

Answer 1

$t=5-y \ge 0 \implies y \le 5$

$ \implies x=2+5(5-y)=-5y+27$

Thus the equation of the plane is $x+5y=27$ with $y \le 5$

Answer 2

Write your System in the form $$x=2+5t$$ $$5y=25-5t$$ and add both.