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Answered 2012-02-29 15:55:11

It means that at least one of the equations can be expressed as a linear combination of some of the other equations.

A linear combination of equations is the addition (or subtraction) of equations. And since an equation can be added several times, it includes multiples of equations.

For example, if you have

x + 2y = 3

and

2x + y = 4

Then adding 2 times the first and 3 times the second gives

8x + 7y = 18

This is, therefore, dependent on the other 2.

If you have n unknown variables, there will be a unique solution if, and only if, you must have a set of n independent linear equations.

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