Hi, good morning. Be okay. Hello, hi. Are you right? Yeah, all is it. Is it where you are in London? No, no, no, no. I'm in China. I'm always here. Actually, it's 3:00. Okay, okay. All right. Okay. So look, let's start with this. A mystery pie chart. Here's the pan. Okay. It's very early in the morning here, so I'm just going to get my a drop more coffee and I'll be you keep thinking, okay. They're feeling a bit stuck. 32. So 32 plus 16 is 48 plus eight plus four nice. Choice c okay. It's 362. 24, 2080, 48. So we need Yeah it's not my key. So you did 215S. I calculated it. Two fifteenths of 360. Yeah so Yeah now 7:20 15 and it was that 240. 240 over five Yeah. Yeah Yeah, that's nice. Okay, very nice. Okay, I was hoping that was going to be a bit challenging, but I think you gave it a little bit of time and you solved it. No problem. Okay, so I promised you this morning we were gonna to look at something called simultaneous linear equations will revise the factoriising as well, but let's start with okay, so basically can you solve this? Okay, the ball is next to an in between the calculator and abbacus. The the abacus, is that a thing? You know the the balls on. Yeah on the number balls on a string like that. Okay. So Oh Yeah, I also think we want to look at something I don't know last time. A backbetween the calculator and goes to the diary, the calcuter, the us and the book cheaper than only right, only right, right, right, right here, total of 20 pound the money next to the end on the immediate right of the. Okay, I think I know which is which now. Okay, I know what you switch. Surprise, I'm surprised that the calcullator so soon, the three only left total. I think it is. This one is the calculator. This one is see. The soon ously x. Diary. Right. And then we want to know how much does it does how much does each thing cost? Okay, calculator. No, here. Left. So wait, just three more. 17. 17. Let me know if you want me to. Sweet. Nine. Eleven eight monkey. I. Hope. Six working. Eleven. 43. 18 but cannot. Nothing. It was not three. It's not two, four, a little bit. I think this about, I just try one moment, minute more, and I'm still stuck out. Ask for help. Yes, I know not. It is six. Six, six. Oh, there's no pound on my tei. Don't know. Six, the. History three bebackus. 哎呦。Add and. Desire me, yes. Okay. Sorry the three on the left because three on the right cost of yes, sorry, I've to just get my left and right confused. So ball abacus diary so very good. But just out of curiosity, did you do anything like this? It's just in terms of forming what we call forming expressions for when it comes to just pure algebra. Okay, so when we want na do just algebra, the calculator costs twice as much as the you could say, okay, we've got b and then in relation to that, the calculator is two b. Did you do that? Yeah, something like but in total therebe three n by. Okay, so because we've got a to B2C to d in terms of price something Yeah but then you could in fact replace c with two b. Okay. What's the reason for that? Yeah. Yeah twice. Also, ababacus costs three pounds more than the diary. So we could say that the diary is d and the abacus is in fact d plus three. Yeah, right. The only reason why we do why that could be useful, I'm not saying there's no other methods, so if you used another method, it's fine. But I just want na introduce that idea to say that's what we call eliminating variables. Okay? So what we're doing, what we're doing is a bit of vote vocabulary. What we're doing there is eliminating variables, okay? Which means instead of we're going from a to b, instead of having A, B, C and d, we are reducing it to just b and d and then we've only got two variables left. Yeah and when you do that, you can compare them in an equation and what we would have prepared. Yeah. So so look here. We've got here. Let's let's try and see if we can get an equation formed. This one, I've learned this rber ten chicken equation is quite, I don't know. Okay. So let's see if we can. Let's see if we can. Let's see if we can do it in terms of R for rabbit numbers of rabbits and c for numbers of chickens. Two variables, rabbits and chickens. How can we form two equations? So if you've already done the problem, let's go straight into the idea of how do we turn this into an equation. Yeah, okay. I there's no message for this one another if minuse. Age 2057. Yeah 57 head and 186 feet. I think my mais a bit different from yours because it's like assuming that all 5057 hatch is rabbit, then if you'll have 200, 228, that's and Yeah and that's yes. Okay, so you're doing it. Okay. So you're doing it by a method that's that's perfectly fine. Okay. But so we're just trying to get this equation method learned. Yeah but I understand what you're saying. What you're saying is what we would call a balancing out method. Yeah. As in as in you've got the right number of heads, right? You could say they're all rabbits, right? 57 heads, okay, that's the right number of heads, but you've got the wrong number of legs is I think what you're saying, right? Yeah. Okay. So you're doing this kind of balancing out method if you reduce the number of rabbits and increase the number of chickens, how many do you need to balance out until you've got the right number of legs? Have I understood rightly or what you're doing? I think it's kind of yes, like 57 times four equal 228, 228-186 equal equals 14, 14, 42, and this 42 divided by four minus two, which is two equals to 21 and that's the number of chickens. Oh Yeah. So you'll reduce so you're saying 21. So you've you've calculated what the reduction in two legs would need to be. Yeah by subtracting by subtracting the two many the right number of legs from the two many legs. Yeah and then you're splitting the difference. Yeah the total number of legs that is extra minus the total number egthey like each. That will be more. So two more legs like rabbit had two more legs like chicken and that's one pair. So it's 228 legs divided by two as each pair. So we have 21 pair. Lovely. Lovely. Okay, so let's just go straight into we're going to do the equation methood so that we can also apply this. Okay, because let's think about I'm sure maybe it does work for minor dumps as well. Anyway, let's just introduce the method. I'm not saying you have to use it every time, okay. But the number of rabbits and the number of chickens is 57. Yeah. Yeah. And the number of rabbit legs I express presses four R Yeah. And the number of chicken legs I express is two c. Yeah Yeah, okay. So we now have 22 what are called simultaneous equations. Okay? So I love the word. I love the word simultaneous. It's got all the vowels of English aou. It's got all of them in it. Simultaneous equation. And that's why I like it. I don't know how many words have got all five vows, but anyway, except for y whnever might be okay. So simultaneous equations, right? So we've got a pair of equations and what it means is we are going to solve them together to get the two answers. Yeah, Yeah and we're going to solve them by subtraction in this case. Okay. So. We know this, okay? And we know this. Right. And what how you can solve both numbers is to subtract the whole of the equation, the whole of the lower equation from the top equation. You're going to subtract four R minus R. Have you done this before? Not really, okay. It's another Oh no, wait, I haven't done this right? Because I didn't notice, I haven't subtracted it fully. You're gonna to double the first equation, just the the lower equation. You're gonna double it. Two R. If you double the whole thing, you've got double of everything two R plus two c equals how much. 114, right? So you double that one because then you're going to do four a, subtract two R leaves you with two R Yeah two c, subtract two c. He nothing 186-114 is 72Yeah and then you see that by subtraction you have eliminated c okay so this back to the Yeah I hope so wonderful but like not in exact the same but the meaning the same like okay listen when I first it and expect to help you legalize those things Yeah okay so we've done the elimination method Yeah where two R is 72 so therefore R is 36Yeah and then just by elimination c 21Yeah Yeah that's many it all worked. I got three on my mind now actually nice. Okay. So. I wanted to show you this method because I think it's a suitable one or doing just pairs of equations. Yeah have you have you been given just pairs of equations like this? Yeah, I think I've done this ones these but okay, do you want to just quickly put the do you want to just quickly put the answers in then let's just check. Okay. Let's put this in. Moment, what else? Mm mm. Is that correct? My parents is acting strange. Wait moment. Delicate. Hi. Okay. Good moment. I think I just out, out time now because my parents keeps slipping away. I got a calculation mistake. That's okay. I thought 35-26 equals eleven. Does? All make sense. Yeah. Y two y equals. And this is two. I be equals. Nine is it? Yes and a. Sky facing. You see. Who doesn't is interesting as negative. 欠你很多的。45. 100 and. 100 and 130 130. 116. Divide. I'm not sure what negative ones with negative. Okay. So this is where the method is helpful. The elimination method that I mentioned here. Okay, right. How it works with negatives is you add them. So basically five e plus five f equals 65. Minus five a plus four f equals seven. Can you add those together? A Vivian? So you get five, five e plus plus minus five e. What is that? Five? Is it five e? You've got ee e and you're going to add negative five e. So you're going, you're going to so there's minus one e. I'm adding minus two e, I'm adding minus three e, minus four e, minus five e. I'm putting those in as well. The negatives, I'm adding the negatives. Got nothing left. Five v plus minus five e. Yeah zero. So when you when you add a negative over, they're subtracting away aren't they? Yeah Yeah okay. And then you add the rest. Okay select my f equals. So remember you're adding you're adding whatever's left so you've got five f add four okay that's nine f. I don't it. Yep. Touch, 嗯。那个。70. Yeah, 70. Two so f is eight Yeah and then you can use f and then you if you use f is eight you can. Yeah if you use f is eight you use you can find out how much e is. It's three. Pardon? Yeah, I'm just going to open the door for my son. Sorry. But I may have to move just because my family are waking up now they were all asleep, okay, so I'm just gonna to move into the other room you right? Okay, so e is three, f is eight nice. Okay, so we've got another negative one there. I'm just going to move whilst whilst you're looking at that last one. I'm still with you, just going into the other room. Okay, here we are. Okay. So. I'll try again again. Oh. So minus 3G. -33. Plus eight equals. Ten 33. Minus seven H. What is so we add those together. And we got nothing. And. -68. Equals minus twelve dies that so that meant H equals two which matters that. 14, 60, 40. Twelve three. 14, two, four nice. Yeah okay, great. I'm happy because something was a little bit challenging. Yeah okay, great. So we see the difference sometimes in methods where obviously negative values of variables are not gonna to happen in any of the rabbit and chicken type problems. Yeah so this is more this is more like just numerical algebraic examples. Yeah and they have examples and we need negatives because these are related as well to the graph of x and y. Yeah. This kind of algebra is stuff that you can graph in two dimensions on x and y. Yeah. And obviously, and obviously over here we haven't got we haven't got gaps. Over here we've got negative. And over here we've got negative Yeah in y. So we need to be able to find those negatives too. Yeah. All right. So then this one is, let's just do one more example. This example, I believe you're going to have to multiply one of the equations. Okay. One of your equations is going to have to get multiplied. Can you see why? It's Yeah Yeah I see why okay. Interest state. 977 3:17 nine 89 8480 48 call seven. That window should be twelve. Can that be right? Alright no action nine y seven calcumistake three. 84-56 is eight, eight, seven, 20 87 and zero three. So to be 6:56, no. Go on. 嗯each。Two. I just want to hear about the acts seem to be weird. Okay, so if y is three. Yeah, then the x is quite weird. Okay, so what I would do Virginia is I would tie sorry, not Virginia. Sorry, Vivian. I've got too many people. Sorry, I've got too many people who start with v Virginia. Veronica Vivian. Okay, right. So I got six x. If I got six x plus two y equals 20x 56. Yeah, Yeah. I'm going to times the second equation by three because that's going to give me six x plus nine y. Yeah equals 84. Yeah, that's as I did. Okay, so then you subtracted. Yeah and I got zero zero sorry Yeah so seven y because is it seven y or minus seven y? Yeah minus seven goes minus yes so y equals three y is 44Yeah four it's another calculation must three okay all so no worries so y is four x is how much. Thatbe eight. Nice. Yeah. 16 yes, okay, lovely. All right. And the next one. 嗯。180 156. 100 and. No. Three. I think this could be this could be any of them times three. So then it becomes a case of which which one, whichever one you prefer. Yeah okay, the bottom one. 36. 72-56. Six. 16. X divide by two equals eight. Eight. No, what? 24. Video, was it? You want me to help, I'll just get it through a bit. I think it just got some calculation, must take maybe on the way. So just check it. So equals to little times is 39x plus nine y and the equals two 72. And so betx one equals to 16 and equequequals to 22. 1:54 divided by nine equals 66 think tage. Ha, so give us six. On 18, Yep, fine. Okay. The other one, okay, this one has to be the bottom. X A plus two b equal of t so it's 16a plus twelve b equals. 140. So ten b equals two, sliso b equals nine. Wait. Goes nine. Goobye. Two a's two. Yeah, very nice. Okay. So look, that's the multiplication method. And then we've maybe just got time just for one more, which is that both equations need to be multiplied. Okay. Because of the difficulty, do you see why both need we have to multiply both right? Because we we can't multiply one easily. Yeah, Yeah, yes, I think understand. Yeah, okay. Y equals seven. Bye. And equal. It's the same. They can be the same number. Yeah which is weird. But if you think about it, it doesn't say x and y cannot be the same. Yeah okay. Because like I said, these are these are related. You don't have to graph them, right? But you could if you wanted to. These are related to straight lines on a graph of y and x. Yeah Yeah. And so if we were thinking about the graph of those two lines, we are thinking about the coordinate 77, right? So obviously, the coordinate 77Yeah, both numbers are the same. Okay Yeah so so it's not it's not weird it's not weird to have two numbers the same because you could have the coordinate pair 77 or 66 or whatever. Yeah and we're gonna to finish there because I need to go straight to another class but basically we're talking about straight lines. Yeah and the solution the solution to the equation is where the two lines cross over. Yeah okay, all right, well done. Fantastic work today, Vivian. Thank you very much. I think you've learned a lot there, so good job. And I'll put this on the board if you want to continue. Okay. Thank you. Bye. Cheers. Bye. Bye.