So I have a small question about inconsistent equations.

So I solved a problem using elimination by addition and turned out with this order pair (4,3) and I had to check it with these two equations

4x-2y=10
6x-3y=-3

I know the pairs work with the first equation but it does not work with the second equation. Does this make this equation inconsistent?

Thanks!

Question

So I have a small question about inconsistent equations.

So I solved a problem using elimination by addition and turned out with this order pair (4,3) and I had to check it with these two equations

4x-2y=10
6x-3y=-3

I know the pairs work with the first equation but it does not work with the second equation. Does this make this equation inconsistent?

Thanks!

anonymous · Answer

Do you anything about matrix algebra?

anonymous · Answer

Nope..

anonymous · Answer

Alright, here is an elementary proof why this two equation is inconsistent.

$ 4x-2y=10 \implies 2x-y=5 $

$ 6x-3y=-3 \implies 2x-y=-1 $

This means that the two equation represents two parallel lines and hence they will never intersect so no solutions.

anonymous · Answer

Ah, I see. Thank you!

anonymous · Answer

Would it possible for you to give me an example of an inconsistent equation?

anonymous · Answer

$ 2x-y=5 $
$ 4x-2y=4$

anonymous · Answer

What about a dependent equation?
Let's say I have an equation that cancels everything out.
-4x-6y=-12
4x+6y=12
Would that be dependent?