Answer: Consistent and independent.
Explanation:
We have the system of equations:
y = 4x - 4
y = -4x + 4.
Now, first let's define the terms used in the question.
consistent and independent: we have only one solution.
consistent and dependent: we have infinite solutions.
inconsistent: we do not have solutions.
Now, let's look at the system:
y = 4x - 4
y = -4x + 4.
Let's take the quotient between both the equations:
(y/y) = (4x - 4)/(-4x + 4)
1 = (4x - 4)/(-4x + 4)
let's see if we can solve this for x.
1*(-4x + 4) = 4x - 4
-4*x + 4 = 4x - 4
-4x - 4x = -4 - 4
-8*x = -8
x = -8/-8 = 1.
and to find the value of y, we can input this value of x in one of the equations:
y = 4*1 - 4 = 0.
Then we have only one solution, (1, 0).
(and will be the same if you input x in the other equation, as the right side is minus the right side of the first equation)
Then the system is consistent and independent.