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

Expert Answers
justaguide eNotes educator| Certified Educator

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.

atyourservice | Student

They are dependent.

baronridiculous | Student

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