What is the difference between linear and homogeneous systems of equations?

[lorik]

Homework Statement

I've been struggling for the past hours and can't find the difference between "linear system of algebric equation " and "homogenus system of equation" ,I have the oral(writting) exam tuesday and I would appreciate a little help since I passed writting exam and only final oral would grant me passage to next semester so Id get rid of so many months of suffering .Thanks all

 

[Raskolnikov]

The word 'homogeneous' entails that all constant terms are zero, which is not required for an algebraic equation.

 

[Mark44]

In a linear system of equations, the variables all occur to the first power, as in this example

x + 2y + 3z = 4
-x + 3y -z = 8

I'm not sure what the "algebraic" part contributes.

In a homogeneous system of equations, all the variables are on one side of each equation and the constants on the right side are all zero, as in

x + 2y + 3z = 0
-x + 3y -z = 0

Now, since it wasn't specified that these are linear equations, we could have systems like this

x² + 2sin(y) + 3z^1/2 = 0
-x + 3cos(y) - 1/z = 0

This is a homogeneous system of nonlinear equations.

Hope that helps.