4 Variable System of Equation

[Asian]

How do you solve a 4 variable system with 4 other systems involved? What is the best apporach in solving it.

 

-Thanks for the Help

[Bluenoise]

I'd say it depends on the systems

[ydoaPs]

If you wanted to, you could use substitution, but it might be a little long for four variables. I'm not sure if you could use a matrix with four or not. I'm sorry I can't be of more help, it's been a while since I've done systems of equations

[Bignose]

If it is linear, a matrix algebra appraoch should be good -- there are certain restraints on whether the matrix is invertable or not, but in the vast majority of time the matrix is invertable.

 

If the system is nonlinear, usually an interative method is necessary, like Newton's method. Once you get a handle on Newton's method, then you can explore various improvements -- almost all of the iterative methods are based on linearizing the system and making an approximate improvement toward a solution. See http://en.wikipedia.org/wiki/Newton's_method

 

As a decent guide, if you are planning on writing computer software to help you solve these systems, computational fluid dynamics (CFD) books are about as good a start as any. A three dimensional viscous flow is a 4 equation non-linear system of equations. (x-velocity, y-velocity, z-velocity, and pressure are all coupled together.) Any good introductory CFD book will have lots of discussions about how to solve coupled systems of equations.