Writing Equations in Two Variables - Free Educational videos for Students in K-12

Writing Equations in Two Variables - By Anywhere Math

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00:0-1	Welcome to anywhere . Math . I'm Jeff , Jacobson
00:02	and Well let's see . We've written equations with one
00:06	variable . We've solved those equations using addition and subtraction
00:11	. We solve them using multiplication and division . Now
00:15	it's time to write equations with two variables . Let's
00:19	get started . So today we're writing equations in two
00:41	variables first . What exactly are we talking about when
00:44	we're saying equations in two variables ? Well uh equations
00:49	in two variables that represents two quantities that change in
00:53	relationship to one another . This word relationships really important
00:57	. What that means is as one of the variables
01:00	change . So does the other variable . They're related
01:04	to each other . You can't change one and not
01:06	the other um Or you can't change one and the
01:09	other one not be affected I should say . So
01:12	now . Well what exactly would a solution to an
01:15	equation like that look like ? Well you've got two
01:18	variables so you're gonna have to values in your solution
01:22	and that solution to an equation two variables is an
01:26	ordered parent . Okay . So commonly like an X
01:34	. Y . Okay . Where each one of these
01:38	uh values would be would work together as a solution
01:42	to your to your equation . Um Let's talk a
01:46	little bit more about what these values are called and
01:50	what they look like . So the two variables in
01:53	these types of equations have names . 1st 1 we
01:56	call the independent variable and that's just the quantity that
02:00	can change freely . Basically we choose what that value
02:04	is for that variable . Okay now the second variable
02:07	we call the dependent variable and just like the name
02:12	. The value depends on what the independent variable is
02:17	. Now that might be a little bit confusing but
02:19	for example here's my favorite mug . Uh If I
02:24	have coffee in this mug and I'm drinking some okay
02:28	and I ask you well how much coffee is left
02:32	you would say ? Well it depends it depends on
02:35	how much I drank already . Right ? So in
02:40	that situation uh the dependent variable would be , what
02:47	is it how much I drink or how much is
02:49	left ? Well the dependent variable would be how much
02:52	is left because how much is left depends on how
02:57	much I already drank , right ? The independent variable
03:01	would be how much I drank , right ? I
03:03	can decide that on my own . I can take
03:05	one sip , I could take two , I could
03:07	do the whole thing . Okay so how much I
03:10	drink would be independent variable . How much is left
03:13	would be the dependent variable because it depends on how
03:17	much I drink . So hopefully that helps keep them
03:19	clear . Now we can graph uh these types of
03:25	these variables and the solutions as an ordered pair ,
03:28	right ? We've graphed ordered pairs before if you're wondering
03:31	which one would be the X . Axis . Which
03:33	would be the Y . Typically uh the independent variable
03:38	, the one that you choose freely . That would
03:41	represent your ex value on the X axis . Independent
03:46	yes . Would be like your ex value and you're
03:49	dependent . Would then be your y depend . Okay
03:56	so if you think you have an order pair typically
03:58	you would say you're independent value first and then you're
04:01	dependent . Okay let's look at example . Alright example
04:05	one tell whether the order pair is a solution .
04:08	So for my first one why it was two X
04:11	. My order pair is 36 . So I'm gonna
04:13	see if that's a solution . If it's a solution
04:15	it should make this equation true . Just like a
04:18	solution to uh an equation with just one variable .
04:22	So to check all I have to do is substitute
04:26	this three is my ex value . So I'm going
04:30	to substitute that three in there and this six is
04:33	my why value ? So I'm gonna substitute in for
04:36	why ? So when I do that I'm gonna get
04:40	I'll do it in red six . And the question
04:45	is that equal to uh two times substitute ? I
04:52	didn't blue the three in for X . So two
04:54	times three . Right ? That's the question . Well
04:58	two times three is six so we have six is
05:01	equal to six . So yes 36 is a solution
05:07	to that . Uh that equation . Now is it
05:10	the only solution ? Right ? That's another question .
05:14	We won't get into that yet . Um But three
05:16	sixes a solution . So let's do the next one
05:19	. Why equals four X minus three . We're asking
05:22	is 4 12 that ordered pair . Is it a
05:24	solution ? You can pause the video and try it
05:27	on your own first . Um Here we go .
05:30	So four again I'm gonna substitute at that in for
05:33	my ex 12 . I'm gonna substitute in for my
05:35	why ? So I get 12 is equal to .
05:40	Well that's the question we're seeing . If it is
05:42	Four times four , make sure you use your parentheses
05:47	, right ? If you don't have them it's gonna
05:49	look like 44 uh minus three . Again . 12
05:54	. Is that equal to ? Well four times four
05:56	is 16 minus 3 . 16 minus three is 13
06:00	. So is that equal to 12 ? No they
06:03	are not equal . Which means 4 12 is not
06:08	a solution . Okay let's do another example . Alright
06:11	here we go . With example too . The equation
06:14	y equals 128 -8 x . gives the amount why
06:19	in fluid ounces of milk left in a gallon jug
06:23	after you pour X amount of cups . Okay uh
06:27	So first part A . Is identified the independent and
06:30	dependent variable . So again independent . That's the thing
06:34	that changes freely . That's the thing that we would
06:36	decide , dependent variables , depend on what you decide
06:42	with the independent what what you do first with the
06:44	independent variable ? Uh So sometimes when you're doing this
06:48	it's easier to find out the dependent variable first .
06:52	So in this situation uh First what are two variables
06:56	? Well we've got Y . And X . Um
06:59	What does that X . Represent for X . Represents
07:02	the number of cups yeah . Of milk that we
07:09	pour out of the jug . Why represents how much
07:14	is left the amount why in food ounces of milk
07:16	left ? So I just write milk milk left .
07:23	So if I think about that Um you might notice
07:27	. Well then if we're subtracting eight X . Where
07:31	did that eight come from ? Right . For example
07:34	if we have one , we poured one cup .
07:37	We multiply by eight . How why would we multiply
07:40	by it ? If you look here why isn't fluid
07:43	ounces ? This isn't cups were multiplying the amount of
07:47	cups times eight . That's because there's eight fluid ounces
07:50	in a cup . Okay Um where is that ?
07:53	128 come from ? We're starting with that . We're
07:57	subtracting out how many cups . So if you think
07:59	well what if I didn't pour any any cups of
08:03	milk out ? Right ? So if that was zero
08:07	Um eight times zero is just zero . So we're
08:09	subtracting zero . That basically goes away and we have
08:12	128 . So that would be the milk left is
08:15	128 fluid ounces . That 128 represents how much is
08:20	in the jug in a full jug ? Right so
08:23	128 fluid ounces in one gallon jug . Okay um
08:28	So that's where those come from , that's where those
08:30	numbers come from , it . Sometimes it helps to
08:32	know that . So anyway let's get back to independent
08:35	dependent variables . What's the thing that depends on the
08:39	other thing ? Do the amount of cups that we
08:43	choose that we pour out ? Does that depend on
08:45	anything ? No that's we choose that up to ourselves
08:49	. How about how much milk is left ? Does
08:50	that depend on anything ? Well yeah , the amount
08:53	of milk left depends on how many cups of milk
08:56	we pour out . So that should tell you that
08:59	the dependent variable is the why ? Yeah . Uh
09:05	huh . Equals the Y . Which is the uh
09:09	the milk left ? Okay . And the independent ,
09:16	what we choose freely is how many cups we pour
09:19	out . So independent then . Yeah , that variables
09:25	the X . Variable . And that's the number of
09:29	cops that we pour out . Okay so that's part
09:32	A . Now part B . How much milk is
09:35	left after 10 cups ? Well again 10 cups that's
09:39	represented by X . In my variables . So If
09:43	X . is equal to 10 , all I need
09:44	to do to find out how much milk is left
09:47	is substitute . So I'm gonna have y . is
09:50	equal to 128 -8 . I'm gonna use my parentheses
09:56	. Uh eight times 10 cups . Well , order
10:01	of operations . I'm gonna do my multiplication first .
10:04	Why equals 1 . 28 minus eight times 10 is
10:07	80 . Now I've got my subtraction . Y .
10:10	Equals 48 . And units . Remember why was in
10:16	fluid ounces ? So 48 fluid ounces of milk left
10:23	. Okay . As pop . You can't I'm sorry
10:25	you can't see that . 48 fluid ounces left .
10:31	Okay so there's my final answer for being here is
10:35	something to try on your own . Thank you so
10:44	much for watching . And if you like this video
10:46	please subscribe

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