Question

Is the system of equations is consistent, consistent and coincident, or inconsistent? y=4x−4y=−4x+4 Select the correct answer from the drop-down menu.

Answer 1

Answer: It is consistent as the lines are intersecting lines and it has a unique solution

Step-by-step explanation:

Since we have given two systems of equation :

$y=4x-4\\\\and\\\\y=4x+4$

We need to check whether the system of equations is consistent or inconsistent.

As we know the formula for checking the consistency :

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

In first equation we have

$y=4x-4\\\\4x-y=4\\\\Here,a_1=4,b_1=-1,c_1=4$

similarly,

In the second equation we have

$y=-4x+4\\\\4x+y=4\\\\Here,a_2=4,b_2=1,c_2=4$

So, According to question, we have

$\frac{1}{4}\neq \frac{1}{-1}\neq \frac{4}{4}\\\\0.25\neq -1\neq 1$

Hence, it is consistent as the lines are intersecting lines and it has a unique solution.

Answer 2

Answer:

The given system of equations is consistent.

Step-by-step explanation:

The given equations are

$y=4x-4$         (1)

$y=-4x+4$           (2)

Add both equations,

$2y=0$

$y=0$

Put this value in 1.

$0=4x-4$

$x=1$

Using the elimination method the solution of given equations is (1,0).

Since the system of equations has a solution, therefore the given system of equations is consistent.