I have simplified my problem below (with Derive 6.0):

t ≔ 0.2

k ≔ 0.1

y = 2·x + 4·t

z = 2·k

x = 2·t

SOLVE([y = 2·x + 4·t, z = 2·k, x = 2·t], [x, y, z])

[x = 0.4 ∧ y = 1.6 ∧ z = 0.2]

I wonder how generalize my problem to be a vector indexed input data.

example:

t(1):=0.2 t(2):=0.3 t(3):=0.4

And get an answer:

x(1) y(1) z(1)

x(2) y(2) z(2)

x(3) y(3) z(3)

Thanks