Simultaneous Equations - Algebra Math Trick - Free Educational videos for Students in K-12

Simultaneous Equations - Algebra Math Trick - By tecmath

Transcript


00:0-1	Welcome to the Tech Math channel . What are we
00:02	having a look at this ? Video is a special
00:04	way of solving simultaneous equations . Now , I've been
00:07	looking at these and other videos , I've been looking
00:09	at the usual way of solving , but this is
00:12	Oh yes , being in the , the spirit of
00:14	the Tech Math channel , which loves looking at ways
00:16	of our solving things using special troops as much as
00:19	we can . This looks at a special trick of
00:21	how you can use solve these fairly rapidly . So
00:25	I'm going to show you how this works . So
00:26	usually what you do is you be this is a
00:29	simultaneous equation . Usually trying to get the numbers in
00:35	front of these particular variables here . The same .
00:39	Okay , So if you're not 100% short of simultaneous
00:42	equation is you might want to check out just a
00:44	couple of back links I'm going to put up now
00:47	. So this is for you guys who are a
00:50	little bit aware of what similar kind of equations are
00:53	, the way that you can solve them really ,
00:55	really quickly using uh this method is this what you
00:59	do is first to work at X . We do
01:02	this we go X equals . Now . We're gonna
01:07	do a bit of a cross , we're going to
01:10	be a bit across more application with the coefficients we
01:13	have here . The first one we're going to do
01:16	is we're going to multiply These two . Okay ,
01:20	two and 26 . We're gonna get the answer 52
01:24	. And from that , we're going to take away
01:28	these ones . Okay , well we'll cross multiply seven
01:32	, 13 . So seven take away seven times 13
01:37	is how much the answer to that is no anyone
01:41	. Okay , So the difference between the 52 or
01:43	91 then , what we're gonna do is we're gonna
01:47	Do the same sort of thing here , we're gonna
01:50	start with these particular ones where we go two times
01:53	four his ID and seven times 3 which is 21
01:59	. We're going to take that from that . Okay
02:03	. You got that method ? Okay . It's really
02:06	really important that you do it . And these are
02:07	this particular order . Okay . So we're going to
02:09	start off I think they're probably the easiest way is
02:12	we're going to start off with this particular one here
02:15	. We're going to multiply it by this . Oh
02:17	my God , it's going to give us this one
02:19	. This one down here is this they came from
02:22	the bottom the one over here is this ? And
02:25	the one over here , is this okay ? So
02:29	50 to take away 91 , you're going to get
02:32	the answer of how much we're going to get ?
02:37	39 Okay minus 39 and then eight take away 21
02:45	. We're going to get the answer of minus 38
02:49	. So these negatives cancel each other out . 39
02:54	13 . We get the answer 39 divided by 13
02:59	3 . So x equals three . That's pretty cool
03:03	method . Right , Okay . You know , it's
03:05	going to take a bit of getting used to .
03:06	How do we get why ? Well , we have
03:08	to substitute into our equation here . So You have
03:12	three x . Is it x equals three , means
03:17	it's going to be dying , dying Plus two .
03:20	Y equals 30 . This means that to why we're
03:25	going to take the one on both sides Equals four
03:29	. That means y equals to just check our answer
03:32	here . So three times four is 12 12 plus
03:37	two . Y . We advise to mediate 14 .
03:39	So 12 plus 14 26 . It's correct . Okay
03:45	, what about what goes for another example here ?
03:48	All right , so I'll rub that out . Uh
03:52	We'll put another example up . Get rid of that
03:58	. We'll get a second example here . What about
04:01	we do ? Um three x plus two . Y
04:08	equals 24 and we have eight X plus three Y
04:17	equals 50 . Okay . So the method we're going
04:21	to be doing that once again , we're gonna be
04:24	starting with this one here . Okay . I'm going
04:26	to get what X equals first so X equals get
04:31	my line here . I'm gonna start here to get
04:34	the ones on this side . I'm going to multiply
04:37	Better change colors . This number body stubborn . So
04:40	100 And to get the 1 um take away from
04:47	this one by this one . Okay . Which is
04:50	24 times three . The answer to that is 72
04:57	. And to get the bottom ones now we're gonna
04:59	go this one by this 1-8 16 . Take away
05:04	313 which was nine . Okay , what do we
05:07	end up with ? 100 ? Take 72 . The
05:09	answer is 28 And 16 Take nine . The answer
05:14	is seven . So 28 divided by seven , the
05:17	answer is going to be four . Okay , substitute
05:21	again once again . So this means by the way
05:23	X equals four . So let's substitute that into our
05:27	equation . Okay . 34 12 . Okay . Plus
05:33	two Y equals 24 . So I'm going to take
05:39	12 . Both sides are going to end up with
05:40	two Y Equals taking 12 . Both sides . 12
05:45	. That means why equal six . So I should
05:49	be able to substitute these values in and see their
05:51	correct . So if X is 448 32 plus If
05:58	six times three is 18 and indeed that does equal
06:02	50 , correct answer . Okay , what about one
06:06	more example ? Okay so let's have a look at
06:12	this example . We have two X . Plus two
06:13	Y . Cause 18 and three X plus 14 Y
06:17	. Equals 49 . Okay so I remember what we
06:21	do X equals . I put this number over and
06:27	we're gonna multiply it once again you're gonna get more
06:29	and more used to these . So two times 49
06:33	It's 98 . And from that I'm going to take
06:36	18 times 14 . Okay 18 times 14 . If
06:41	you remember how to do this , I have a
06:42	video on how to do this Really really rapidly and
06:46	hopefully the answer you're going to get is going to
06:48	be 200 and 52 . Okay . What we have
06:55	next is three twos six and 14 times two Which
07:03	is 28 . Okay . So what we're gonna get
07:08	98 to take away 252 we get the answer of
07:12	154 orders and six take away 28 leading at the
07:20	answer of Morris 22 . Okay , we can actually
07:25	cancel these two negatives out Just to make it look
07:29	a bit prettier . Um 154 divided by 22 .
07:34	We can even council that down if we want to
07:36	make it a bit nicer . So this will become
07:38	11 , divide both sides by two . This site
07:41	here is going to become 77-77 over 11 X equals
07:48	seven . Okay , it's actually called seminar substitute values
07:53	in now into this first equation . So two times
07:56	X . It's 14 . 2 times seven is 14
08:00	plus two . Y equals The case to two .
08:06	Y . take 14 on both sides . I'm going
08:09	to get the answer before . Okay , 14 off
08:13	18 is four and that means why Therefore equals two
08:18	. So our two answers x equal seven vehicles to
08:22	substituted into equation to just to double check . So
08:27	seven times 3 is 21 Plus 14 times Y ,
08:32	which is 28 . Indeed the answer is 49 .
08:37	It's pretty cool method A It's a good little math
08:39	trick . Um Now , just a few little things
08:42	you may wonder with this um which you might have
08:44	picked up along the way and that's some of the
08:47	ordering issues that might occur . Okay , I'll show
08:51	you what I mean by that . So let's just
08:53	say I'll get rid of these ones here . Yeah
08:59	. What you might realize when you're doing these is
09:01	this if you can do X . What you can
09:04	also do for this , is that why back there
09:08	has disappeared in my rubbing out . What you can
09:10	also do is you can actually , it's not really
09:14	really that important . Which one you take away from
09:18	which one first , but as long as you're fairly
09:20	consistent share what I mean by this , say I
09:23	had decided to do this one first . Okay .
09:27	14 times 18 . Which is again Uh 2 52
09:34	and I took this one offered which is going to
09:38	die . Okay , that's forward . As long as
09:42	I started down here , last time I start here
09:44	this time , so 14 to 28 and I'm taking
09:51	three times 2 , which is six , I still
09:53	get the right answer , but the major thing to
09:55	remember is for these ones , so on the left
09:57	hand side , you either want to start on the
09:59	bottom , all on the top . Okay . It's
10:03	pretty cool method . Anyway , anyway , I hope
10:04	you like that . Uh any comments ? Any suggestions
10:09	? So next time .

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