Question: getting parametric equations

Hello Maple users friends,

I have two lines in the space (x,y,z) described by the equations in L1 and L2:

 

L1:= {4*x + 3*y + z = 0, x + y - z - 15 = 0}:

L2:={12*x + 5*y + 7*z -13 = 0, 9*x + y -3*z - 5 = 0}:

I would like the get the parametric (with z=t) equations P1 and P2 of the two lines..

I see the "form" of such parametric equations P1 and P2 using "solve"

solve(L1, {x, y}); solve(L2, {x,y});

 

but I do not know how to use those values to get my parametric equations P1 and P2 to continue with additional computation (area, volume etc).

Thanks for your attention and help.

JJ

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