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

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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.**

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

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