Question

Is the system of equations consistent and independent, consistent and dependent, or inconsistent?

y=4x−4y=−4x+4

Select the correct answer from the drop-down menu.

(a) consistent and independent
(b) consistent and dependent
(c) inconsistent

Answer 1

(b) consistent and dependent

Explanation:

The given system is

`y=4x-4\\y=-4x+4`

If we sum these equations, we would have

`2y=0\\y=0`

Then, we use this value to find the other

`y=4x-4\\0=4x-4\\4=4x\\x=1`

So, the system has a unique solution of
`(1,0)`.

Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called independent.

Therefore, the given system is consistent and dependent.