Question

Check my answer please. Without graphing, is the system independent, dependent, or inconsistent?
y=2x-8
2x-y=8
A: dependent
B: independent
C: inconsistent
I think the answer is B independent because it has aleast one solution.

Answer 1

No need to post it twice

Answer 2

Here's the thing. Your first given equation is:

y = 2x - 8

If you subtracted y from both sides, then added 8 to both sides you'd have:

8 = 2x - y

Which is the same as the second equation. In other words, both equations are the same thing.

Answer 3

If two linear equations equivalent, then they represent the same line. Thus the system is dependent.

Answer 4

A dependent system means it has infintely solutions, so the equations is consistent havibng many solutions being one line if it was graphed? because i thought it was dependent but second guessed myself.

Answer 5

@hero were u go

Answer 6

Yes, if you have two equations that represent the same line, then of course there are infinite solutions because every point you test will be the same for both equations.

Answer 7

For example, we know that (0,-8) is a point on the first equation. Now let's test it for the second equation:

2x - y = 8
2(0) -(-8) = 8
8 = 8

True

If you tested another point, it would also be true. No matter how many points from the first equation you test, it will be true for the second equation. Thus, infinite solutions. Thus dependent system.

Answer 8

Thank you so much :)