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

The given system of equations is consistent.

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.

Answer 2

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

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 :

`(a_1)/(a_2)=(b_1)/(b_2)=(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

`(1)/(4)\\eq (1)/(-1)\\eq (4)/(4)\\\\0.25\\eq -1\\eq 1`

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