# Solve and a system of equations with a parameter

I've been struggling with this a bit. I've been googling in search for an answer but failed to do so. I want to solve this system of equations with a parameter

Solve[
{x == light[] + (i[] - light[]) t,
y == light[] + (i[] - light[]) t,
z == light[] + (i[] - light[]) t,
Z == 0},
{x, y, z}]


In the end to get the answer i wanted i just got rid off variable z and used something like this

Solve[
{x == light[] + (1 - light[]) t,
y == light[] + (2 - light[]) t,
0 == light[] + (1 - light[]) t},
{x, y, t}] // N


But it bugs me, is there a way to get the same answer using more readable and flexible code which presents the equation in a more general way (something which looks closer to my first attempt at this Solve). And sorry if my english is weird, not my first language.

• Mathematica cannot solve your first Solve command, because it cann't fullfill the equation Z==0Perhaps itshould be z==0? – Ulrich Neumann Nov 23 '18 at 20:08
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• You have 4 equations and 4 unknowns, just need to solve for all of them. Ulrich has it correct, below. – MikeY Dec 23 '18 at 22:24

Assuming the last equation z==0 you can solve your equations for x,y,z,t
Solve[{x == light[] + (i[] - light[]) t,