Question

How do you solve systems of equations by graphing? Here are my 2 problems: 5x+2y=0 & x+2y=8

Answer 1

Do you know how to find x and y intercepts?

Answer 2

No, I don't think so.

Answer 3

Well x intercept: when y =0
y intercept: when x=0

For the first one theyre both gonna come out intersecting the origin, and you cant make a line from that. So instead for that one lets put it in the form y=mx+c and use the slope/y intercept to graph

Answer 4

Ok, but would this solve my equations? Because I have to plot each equation and then figure out where they intercept.

Answer 5

Yes this will let you graph it.

So for 5x+2y=0 isolate the y on the left and we get

2y=-5x+0
y=-5/2x+0

so you can see the slope is -5/2 and the y intercept is 0
Can you graph that now?

Answer 6

Yes, thanks. So, on x+2y=8 , the y intercept would be 8, right? But how to you get the slope on this one?

Answer 7

Would x=1?

Answer 8

If you want to do that one like the last one, just get y all by its lonesome on the left.

x+2y=8
2y=-x+8
y=-1/2x+4

Can you now see what the slope and y intercept is?

Answer 9

The slope is -1/2 and the y intercept is 4. But how to you get the slope? I just don't get it.

Answer 10

Whatever the number in front of the x is after you isolate the y on the left side is your slope

x+2y=8

we subtract x from both sides

2y=-x+8

Then divide both sides by 2

y=-1/2x+4

Answer 11

Oh, thanks! When you graph it, you would go up 4, then down one and over two?

Answer 12

I don't follow...The y intercept on this one is 4, right? so plot (0,4) and from that point go down 1 then right 2 since your slope is -1/2. Plot that point and then draw a line through the two points

Answer 13

Yeah, that is what I was saying.
So, on the other one you would plot (0,0) and then go down 5 and right 3, correct?

Answer 14

Down 5, right 2.

And of course the point where they intersect is your solution. I think you already knew that

Answer 15

Wow, thanks soooo much. I was really lost, but thanks! :D

Answer 16

You're welcome

Answer 17

One more question though. With 6x-10=y , how would you do that?

Answer 18

How would you graph it, is that what you're asking?

Answer 19

I mean how to solve. The y is already isolated, but how do you solve the rest?

Answer 20

Im not understanding what you mean....do you wanna find what the slope and y intercept is?

Answer 21

Alright, its just ordered different. remember the number in front of the x is the slope, and the constant is the y intercept. What do you think it would be?

Answer 22

Okay... The slope would be -1/6, I think, and the y intercept is 10?

Answer 23

Close...Number in front of the x is 6, so slope=6

the constant is -10 so y intercept is (0,-10)

Answer 24

Ok, I'm getting the hang of it. So you would plot (0,-10) but with 6, how would you plot that?

Answer 25

Think of it as 6/1 so from (0,-10) go up 6, right 1

Answer 26

ok, thanks!

Answer 27

you're welcome

Answer 28

How would you solve 0.5x-4=y and -2.5x-2.5=y ?