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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)

[00:00:00] -0.7x +0.6y =1.3 0.5x -0.3y = -0.8

Amanda W (Tutor)

[00:00:12] Hi, welcome to tutor.com !

[00:00:34] I see the problem you've written.
Can you tell me the directions for it, please?

Guest (Customer)

[00:01:53] solve for x and y is all i know
to do

Amanda W (Tutor)

[00:02:09] Ok, are you supposed to use a specific method?

[00:03:20] Like substitution or linear combinations?

[00:03:51] (also called addition method or elimination method)

Guest (Customer)

[00:04:06] substitution

Amanda W (Tutor)

[00:04:22] Ok, great!
Let me write the equations on the board for us.

Guest (Customer)

[00:04:51] ok

Amanda W (Tutor)

[00:05:23] Ok, can you read that ok?

Guest (Customer)

[00:05:37] yes

Amanda W (Tutor)

[00:05:56] Alright, let's get started!
Do you have an idea of what to do first?

Guest (Customer)

[00:06:19] nope not at all

Amanda W (Tutor)

[00:06:38] Ok, well what do you notice about all those numbers?
Do they have something in common?

Guest (Customer)

[00:07:16] the x and y's

Amanda W (Tutor)

[00:07:44] OK, good.
I noticed that they all have one decimal place.

[00:08:20] I don't know about you, but any time I can rewrite a problem without decimals, I think it's a little easier to work with.
Do you agree?

Guest (Customer)

[00:08:29] yes

Amanda W (Tutor)

[00:08:57] Ok, can you think of something we can multiply both sides of each equation by in order to move the decimal place over once?

Guest (Customer)

[00:09:22] 10?

Amanda W (Tutor)

[00:09:32] That's right!
Do you want to try it?

Guest (Customer)

[00:10:24] -7x +6y=13

[00:10:40] 5x-3y=-8

Amanda W (Tutor)

[00:11:20] Good job.
Ok, so now in order to use the substitution method, we need to choose one variable (x or y in either equation) to get by itself.

Guest (Customer)

[00:11:35] ok

Amanda W (Tutor)

[00:11:58] Ok, so which variable would you like to choose?
blue x, blue y, red x, or red y?

[00:13:07] It doesn't really matter which one you choose, we can work with any of them.

Guest (Customer)

[00:13:43] blue x

Amanda W (Tutor)

[00:13:51] Ok, great!

[00:14:16] So what can we do to get this x by itself on one side of the equal sign?

[00:14:57] Just let me know if you're not sure.

Guest (Customer)

[00:15:23] subtract 7

[00:15:28] add 7*

Amanda W (Tutor)

[00:15:50] Not quite.
Let's focus on getting rid of the y-term first.
Do you know how to move it?

[00:16:51] Let me know if you need help with that

Guest (Customer)

[00:17:25] ok

[00:17:49] could we add both equations
together

Amanda W (Tutor)

[00:18:11] Instead of using the substitution method?

[00:18:59] It sounds like you'd like to use the addition (also called elimination) method.
Is that right?

Guest (Customer)

[00:20:10] which ever one is quickest

Amanda W (Tutor)

[00:21:09] OK, let's try the addition method.
In order for you to add the two equations together, one set of variables has to be opposites.
Is there a way you can change one of the equations to make opposites?

Guest (Customer)

[00:21:44] im not sure

Amanda W (Tutor)

[00:22:48] Ok, let's think about -7x and 5x versus 6y and -3y.
Which would be easier to make into opposites of the same number?

Guest (Customer)

[00:23:22] 6 and 3

Amanda W (Tutor)

[00:23:33] Right, so what can we do to make them opposites?

[00:24:28] How can we change the -3 into a 6?

[00:24:44] or rather -6?

Guest (Customer)

[00:25:36] by 2

Amanda W (Tutor)

[00:25:55] That's right, so we need to multiply the red equation (both sides) by 2.
Want to try it?

[00:27:12] Let me know if you need some help.

Guest (Customer)

[00:27:31] 5(2) -3(2)=-8?

Amanda W (Tutor)

[00:28:10] That's the right idea.
You need to make sure you keep your x and y in the equation, and also multiply -8 by 2.

[00:28:24] 5(2)x-3(2)y=-8(2)

[00:28:37] And what do you get if you multiply each of those?

Guest (Customer)

[00:29:55] 10x-6y= -16

Amanda W (Tutor)

[00:30:14] Ok, great!
So let me write that for you.

[00:30:47] Alright, we're ready to add the equations together.
Can you do that step?

Guest (Customer)

[00:32:12] 3x+0y=3

Amanda W (Tutor)

[00:32:34] That's close.
What's 13+(-16)?

[00:33:37] Not positive 3, but...?

[00:34:18] Let me know if you're not sure.

[00:34:52] Are you still there?

[00:35:36] I'll only be able to wait for a few more minutes. If I don't hear from you soon, I'll need to end this session so I can help other students. You can sign back in when you are ready to continue working.

Guest (Customer)

[00:35:48] im here

[00:35:57] -3

Amanda W (Tutor)

[00:36:04] Right, it should be -3.

[00:36:14] Can you find x from here?

Guest (Customer)

[00:36:44] -yx=0

[00:36:47] x=0

[00:36:52] or -3

Amanda W (Tutor)

[00:37:09] Not quite.
What do you have to do to get x by itself?

Guest (Customer)

[00:37:43] subtract the 3 in front

Amanda W (Tutor)

[00:38:11] You would subtract if the 3 was being added, but it's being multiplied.
So how would you undo that?

Guest (Customer)

[00:39:15] divide

Amanda W (Tutor)

[00:39:25] That's right.
so what does that give you for x?

Guest (Customer)

[00:39:32] x=-1

Amanda W (Tutor)

[00:39:37] Very good.

[00:40:01] Ok, now we need to find y.
Do you know how to do that?

Guest (Customer)

[00:40:46] y=-3?

Amanda W (Tutor)

[00:41:11] That's not what I got.
Can you tell me how you found your answer?

[00:42:50] Are you still there?

Guest (Customer)

[00:43:22] yes

[00:44:00] i just subtracted the 6y's and
put y infront of the -3

Amanda W (Tutor)

[00:44:52] OK, what we need to do is use the fact that we know x=-1.
You can take that value and plug it in for x in either the blue or red equation.
Then you can get y by itself.

Guest (Customer)

[00:46:21] -7(-1) +6(-1)=13?

Amanda W (Tutor)

[00:46:53] That's close.
You can plug it in for x, but not y, so it should look like this:
-7(-1)+6y=13.

[00:47:42] Can you solve this equation for y?

Guest (Customer)

[00:48:51] 7+6Y=13

Amanda W (Tutor)

[00:49:03] That's a great first step.
What's next?

[00:50:27] Let me know if you need some help.

Guest (Customer)

[00:50:53] do we subtract 7 and subtract
it from the 13

Amanda W (Tutor)

[00:51:06] Yes, that's right.
Let me know what you get when you do that.

Guest (Customer)

[00:52:38] 6y=6

Amanda W (Tutor)

[00:52:53] Great!
One more step! What do you get for y?

[00:54:05] Let me know if you need some help.

Guest (Customer)

[00:54:39] y=0

Amanda W (Tutor)

[00:54:51] Not quite.
Remember, you need to divide, not subtract.

Guest (Customer)

[00:56:01] y=1

Amanda W (Tutor)

[00:56:27] You got it!
So x=-1 and y=1.
Does that answer your question?

Guest (Customer)

[00:58:14] yes

Amanda W (Tutor)

[00:58:32] Ok, I see that you don't have any more questions, so thanks for using tutor.com !
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Have a good night!