Question

~Medal+Fanning~
Select the system of equations that corresponds to the given graph.

4x + 2y = 12
4x + 2y = 4
2x + 3y = 4
6x + 9y = 12
2x + 4y = 12
2x + y = 3
2x + 3y = 8
−x + y = −4

Answer 1

@Directrix

Answer 2

It looks as if the two equations in the systems of the answer options combine to be just one line. That is, there is only one line shown in the posted graph.

Answer 3

@HelloGoodmorning What do you think could or would cause that?

Answer 4

I'm not the best at these I only know know that it being on the same line is infinitely many solutions @Directrix

Answer 5

Hey, that's a big clue.

When two different lines intersect, they intersect in a single point. That is one solution.

If you have infinitely many solutions, the two line equations are the same but just look different at first glance.

Answer 6

So, look at the answer options and see if any two of the equations in an option are really the same equation in disguise. I'll do an example to show you what I mean by that.

Answer 7

Okay!

Answer 8

I am starting with option D.

2x + 3y = 8
−x + y = −4

These look as if the second equation might have been multiplied by 2 to get the first one.

Let's check.

Answer 9

Okay.

Answer 10

2x + 3y = 8 --> --> 2x + 3y = 8
−x + y = −4 --> Multiply by 2 --> -2x + 2y = -8

@HelloGoodmorning Are these two equations identical in every number.

Answer 11

No

Answer 12

Right. So, look at option C. Do those equations look like they could be made to be identical in every number?

Answer 13

Let me check

Answer 14

We're looking at these:

2x + 4y = 12
2x + y = 3

Answer 15

Ok question How do I know if they're in disguise

Answer 16

@Directrix

Answer 17

Can you make one look like the other? Multiply the second equation by 2 and see if it becomes the first equation.

2x + 4y = 12

2x + y = 3

Answer 18

No.

Answer 19

Correct. They both had 2x in them so when you try to get the y terms and constant terms to be the same, the x terms are changed.

Now, we go to option B.

Answer 20

2x + 3y = 4---> Multiply by 3 ---> ? @HelloGoodmorning

6x + 9y = 12

Answer 21

Okay and we multiply it by 2

Answer 22

Oh okay 3

Answer 23

3

Answer 24

Hey! It looks like b is it

Answer 25

Yes! Hey, I want you to see what happens when these are graphed.

Just a second.

Answer 26

Okay sure thing!

Answer 27

Click on this link:
http://www.wolframalpha.com/input/?i=+2x+%2B+3y+%3D+4%2C+6x+%2B+9y+%3D+12+

Answer 28

That is the graph of the two equations from option B.

We could have entered the equations of all the options to see which one produced the graph you were given in the problem. But, we used a better approach, I think.

Answer 29

Wow good website and that's okay you taught it very well and also I gave you a testimonial earlier because you always help me!

Answer 30

Yes, I saw that. Thank you very much. It means a lot to me.

Answer 31

No Problem :) Thanks for helping again.

Answer 32

You are welcome.