Question

Select the system of equations that corresponds to the given graph.

My answer is
-8x + 4y = -16
-4x + 2y = -8

Am I right? :)

Answer 1

I recommend downloading geogebra to graph this

Answer 2

Do you notice something about those 2 equations? Something about how they compare to one another?

Answer 3

They are parallel?

Answer 4

Well, you can certainly IF they are parllel. What about them, would make them parallel?

Answer 5

I used geogebra and got this graph

Answer 6

They a right beside each other and they will never cross?

Answer 7

yes what I just posted has one line right on top of the other

Answer 8

Don't need any software for this. Just need to understand about the nature of the equations of line. I'm certain that the intent of the question is NOT to graph it in a software package. it's to understand the concept.

Answer 9

that's true, but it helps to have something to check

Answer 10

Ok, yes, parallel will never cross. But what about the EQUATIONS would make them parallel?

Answer 11

Thanks @jim_thompson5910 I'll download it

Answer 12

as DebbieG is saying, don't rely 100% on it

it's just something there to check your work

Answer 13

Im not getting what your trying to show me @DebbieG

Answer 14

OK, if the line equations were in y=mx+b form, what tells you that the lines are parallel?

Answer 15

Let's take another approach. :) In a linear system of 2 equations, there are 3 possibilities:

1. two distinct lines that cross at 1 point - one solution
2. two distinct lines that never cross (parallel) - no solutions
3. two equations for the SAME LINE, e.g., only 1 line because the 2 equations are equivalent. Infinitely many solutions, because every point that satisfies ONE of the equations, also satisfies the other (well, yeah.... they are the SAME line)

Answer 16

Do you know what to look for in the system to tell which KIND of system you have? That's what this problem really wants to know, I think.