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#### datahead8888

##### New member

- Jul 24, 2013

- 4

2x + 3y + 4z = 1

3x + 4y + 3z = 2

4x + 5y + 3z = 3

It has numerical constants in front of each term. You could use Gaussian elimination and solve for one, infinite, or no solutions. (The above example is completely random). It works because you can cancel terms out.

It's a bit less straightforward to find information on how to solve it when you have constants represented by symbols:

ua*x + ub*y + uc*z = 1

va*x + vb*y + vy*z = 2

x + y + z = 3

Here we want to solve for x, y, and z, each expressed in terms of ua/ub/uc/va/vb/vc only. You can't use elimination here because terms such as ua and va will not cancel out. (This example is slightly random too - I just need to learn the technique).

The only method I'm aware of is substitution, though it seems to spill onto multiple pages (the above system is simpler than what I need to solve). Is there any easier way to attack something like this? Any links to online references would be much appreciated.