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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

Respuesta :

ahmadeasterling

Answer:

b

Step-by-step explanation:

Answer:

(b) consistent and dependent

Step-by-step explanation:

The given system is

[tex]y=4x-4\\y=-4x+4[/tex]

If we sum these equations, we would have

[tex]2y=0\\y=0[/tex]

Then, we use this value to find the other

[tex]y=4x-4\\0=4x-4\\4=4x\\x=1[/tex]

So, the system has a unique solution of [tex](1,0)[/tex].

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.

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