How do you convert an ordinary equation into a parametric equation? [duplicate]

Question

It's a 3D linear equation {P1: 2x-y-3z+2=0,P1: x+2y-z-6=0}

Are there any methods that can convert this linear equation to its parametric form.

Ps:the parametric form is {x=7t, y=-t+14/5, z=5t}

Answer 1

You can use Solve to eliminate variables

eqs = {2 x - y - 3 z + 2 == 0, x + 2 y - z - 6 == 0}
{x, y, z} /. Solve[eqs, {x, y}][[1]] /. {z -> t}

Out[1]= {2 + 2 x - y - 3 z == 0, -6 + x + 2 y - z == 0} 
Out[2]= {1/5 (2 + 7 t), (14 - t)/5, t}