Without graphing, is the system independent, dependent, or inconsistent y=2x-8 2x-y=8

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Question:

Without graphing, is the system independent, dependent, or inconsistent y=2x-8 2x-y=8

Answer:

An independent system has different slopes hence has a unique solution.

If two lines have the same slope then, they are inconsistent. The reason is that the two lines could have NO SOLUTION or INFINITELY MANY SOLUTION.

An inconsistent system that have infinitely many solution is said to be dependent.

Now let us make ?f=y the subject in both equations, to obtain,

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?f=y%3D2x 8

For the seccond equation, we have

?f=2x y%3D8

?f=%5CRightarrow%20 y%3D

?f=%5CRightarrow%20y%3D2x 8

Wow, the two systems have the same slope and ?f=y intercept. This means the system has infinitely many solution, hence it is dependent.

The two systems are dependent

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