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State whether the following equations are independent, dependent, consistent,...

spock3's profile pic

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State whether the following equations are independent, dependent, consistent, inconsistent: 4x + 8y = 2 and x + 2y = 1/2

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justaguide's profile pic

Posted (Answer #1)

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The equations given are: 4x + 8y = 2 and x + 2y = 1/2.

Plotting the lines represented by the two equations gives:

Both the equations give the same line. The equations have an infinite number of solutions.

The equations that are given are consistent but dependent.

baronridiculous's profile pic

Posted (Answer #2)

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Notice that the first equation is exactly the second equation multiplied by 4 on both sides.  So this system is dependent.

atyourservice's profile pic

Posted (Answer #3)

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They are dependent.

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