Question

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

Answer 1

Answer: Consistent and independent.

Step-by-step 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.