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# What is consistent and dependent?

Natoyab

Lvl 1
2010-11-22 22:53:24

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 = 8

4x + 8y = 16

Solve the first equation for x:

x = 4 - 2y

Plug 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 = 8

4x + 8y = 15

Solve the first equation for x:

x = 4 - 2y

Plug 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.

Wiki User

2010-11-22 22:53:24