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.
They are dependent.
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