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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.

Q: What is the meaning of a system of linear equation that are dependent?

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No....not necessary

if a dependent system of equation is solved, how many solutions will there be?

Yes

When its matrix is non-singular.

dependent

Related questions

It is a system of linear equations which does not have a solution.

The terms consistent and dependent are two ways to describe a system of linear equations. A system of linear equations is dependent if you can algebraically derive one of the equations from one or more of the other equations. A system of linear equations is consistent if they have a common solution.An example of a dependent system of linear equations:2x + 4y = 84x + 8y = 16Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 16, which gives 16 = 16.No new information was gained from the second equation, because we already knew 16 = 16, so these two equations are dependent.An example of an inconsistent system of linear equations:Because consistency is boring.2x + 4y = 84x + 8y = 15Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 15, which gives 16 = 15.This is a contradiction, because 16 doesn't equal 15. Therefore this system has no solution and is inconsistent.

No....not necessary

One equation is simply a multiple of the other. Equivalently, the equations are linearly dependent; or the matrix of coefficients is singular.

if a dependent system of equation is solved, how many solutions will there be?

A dependent system is defined as "a system of equations that has infinite solutions." It is an equation that is used in various mathematical situations.

Yes

a linear equation

When its matrix is non-singular.

dependent

This is a linear algebra question and it is incomplete since there are no equation which have to be solved.

By elimination and substitution