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Consistent and Inconsistent Linear Systems

Systems with parallel or intersecting lines

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Who Done It?

Have you ever wondered how police use eyewitness statements to solve crimes? After interviewing several witnesses, it might at first seem impossible to find out “whodunit,” but if investigators think of the collection of statements as a system of equations, they can start to put together the pieces of the puzzle.

Why It Matters

If one witness says the bad guy has black hair and is a man, while another one insists the criminal is female and blond, their statements are inconsistent. Based on these two statements, no conviction can be made. If two eyewitnesses both say that the criminal is an elderly gentleman with gray hair, a conviction still can’t be made. That’s because these are dependent statements.

To make a conviction, an officer of the law needs two independent statements that are consistent with each other. For instance, “The bank robber was middle-aged man with a red beard,” and “The man who held up the bank was had a tattoo on his left arm.” This same principle applies to system of equations: whether the equations are consistent, inconsistent, dependent, or independent will determine the number of solutions.

Take a look at what happens when inconsistent statements are given in court:

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Watch the video below to learn more about how forensic scientists use witness testimony to solve crimes.


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