Mastering Equation Solving: 3 Ways to Simplify Complex Equations

[yoyochan]

(3*10^8 t - 19288.47)^2 = (x-18167.44)^2 + (y-38037.28)^2 + (z-433.35)^2
(3*10^8 t - 17862.46)^2 = (x-40607.42)^2 + (y-11317.32)^2 + (z-5.077)^2
(3*10^8 t - 69656.18)^2 = (x-40607.42)^2 + (y-11317.32)^2 + (z-5.077)^2
(3*10^8 t - 14143.42)^2 = (x-24729.37)^2 + (y-34126.78)^2 + (z-930.27)^2

 

[NascentOxygen]

(3*10^8 t - 19288.47)^2 = (x-18167.44)^2 + (y-38037.28)^2 + (z-433.35)^2
(3*10^8 t - 17862.46)^2 = (x-40607.42)^2 + (y-11317.32)^2 + (z-5.077)^2[/color]
(3*10^8 t - 69656.18)^2 = (x-40607.42)^2 + (y-11317.32)^2 + (z-5.077)^2[/color]
(3*10^8 t - 14143.42)^2 = (x-24729.37)^2 + (y-34126.78)^2 + (z-930.27)^2

You are wanting to solve these simultaneously? Where did these come from?

Are you sure the RHS of two lines is supposed to be identical?

 

[Maged Saeed]

It is strange equations..
But I think you can do it by matrices ..
Can't you!

 

[NascentOxygen]

It is strange equations..

That's why I'm curious to know where they arose.

Are there any other constraints on the solutions?

But I think you can do it by matrices ..

Have you looked into this, and tried solving by any means? Others are more inclined to offer help if they can see you have at least made some attempt at solving it by your own effort.

Do you have in mind how many sig figs you would like in the answers?

If all you are interested in are the solutions, have you tried wolfram alpha?