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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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Are system of equations and system of linear equation the same?
No....not necessary
If a dependent system of equations is solved how many solutions will there be?
if a dependent system of equation is solved, how many solutions will there be?
Is there any system which involves one nonlinear equation and one linear equation?
Yes
When will the system of linear equation be consistent?
When its matrix is non-singular.
If a system of linear equations has many solutions what would be the correct mathematical description of the system?
dependent
