| 00:00:05 | Stand up. |
| 00:00:18 | Good afternoon, class. |
| 00:00:19 | E:00] |
| 00:00:25 | While I am taking roll, put away all the things you are passing around as soon as possible. |
| 00:00:39 | Lo Pak Man? Chan Ka Cheong, Lo Pak Man, report to Room 201 on the twenty-first of this month, Wednesday, at 7:30 a.m. |
| 00:00:48 | Otherwise the two of you will have disciplinary punishment. Is Chan Ka Cheong here? |
| 00:00:53 | Pass the paper to him to see. |
| 00:00:59 | Yeung Wan Chi. |
| 00:01:00 | Is absent. |
| 00:01:01 | Is absent? Who else? |
| 00:01:04 | We have only one absentee? |
| 00:01:13 | Can any of you turn in the new book today? |
| 00:01:16 | Anyone? |
| 00:01:17 | Yes you hear. |
| 00:01:18 | If yes, you can... how many are there? |
| 00:01:21 | Next time I'll tell oh! |
| 00:01:23 | Only the two of you? |
| 00:01:24 | Two. Okay, just bring it in tomorrow. Just the two of you... |
| 00:01:30 | Why are you so late? |
| 00:01:31 | (inaudible) |
| 00:01:33 | What? |
| 00:01:34 | I was washing the glasses. |
| 00:01:38 | Are you ready? Open your books. |
| 00:01:48 | Before we start on a new topic today, we will take a look at what we have done yesterday. |
| 00:02:00 | Yesterday, we should have stopped on 22, right? |
| 00:02:02 | (inaudible) |
| 00:02:05 | How can it be number 24? |
| 00:02:06 | Twenty-two. |
| 00:02:07 | Twenty-three. |
| 00:02:08 | There is a star next to number 23. I did not tell you to do it. |
| 00:02:13 | First of all, are there any special questions? |
| 00:02:16 | No. |
| 00:02:17 | Are there? |
| 00:02:18 | No. |
| 00:02:19 | Raise your hand if you have questions. |
| 00:02:21 | If not, I will ask some of you to come up and try some of the questions. |
| 00:02:28 | Are there any questions on question number 20 with the star? |
| 00:02:29 | No. |
| 00:02:30 | There is nothing special about it, right? It did not look too special. |
| 00:02:33 | [ Bell ] |
| 00:02:34 | Uh, let's do number 20 then. |
| 00:02:35 | (inaudible) |
| 00:02:40 | Twenty-one and 22 are both very easy, right? |
| 00:02:44 | Yes. |
| 00:02:45 | Uh... |
| 00:02:46 | Twenty-three. |
| 00:02:54 | Twenty... how about doing number 19 and 20? |
| 00:03:02 | Fung Cheuk Yue, do number 19. |
| 00:03:22 | Cheung Lung Man, do number 20. |
| 00:03:42 | Our class is being taped today, therefore, the light is turned off to avoid reflections. You may have a hard time looking at the blackboard. |
| 00:04:26 | Are you in a hurry? |
| 00:04:28 | (inaudible) |
| 00:04:29 | Which is the last question you have finished? |
| 00:04:30 | This one. |
| 00:04:31 | Which question did I tell you to do? |
| 00:04:33 | (inaudible) |
| 00:04:40 | So? |
| 00:04:41 | I am thinking. |
| 00:04:42 | Don't, don't tell me that you don't know how to do them. |
| 00:04:44 | Okay, I am thinking. |
| 00:04:46 | Don't do them when I am teaching later, okay? |
| 00:04:48 | Okay. |
| 00:04:49 | Stay here when class is over. |
| 00:04:50 | Umm. |
| 00:04:51 | Did you hear me? Stay after class. Finish them for me when you stay after class. |
| 00:05:02 | I don't know how to do number 20. Can you teach me? |
| 00:05:08 | How to do number 20? There is nothing special about this question. |
| 00:05:11 | (inaudible) |
| 00:05:13 | Um... that will work too, but you will have an extra sign. Don't you think it will make it look terrible with that extra sign? |
| 00:05:25 | Alternatively, you don't have to take the two T as the subject. |
| 00:05:28 | You can take the T as the subject. Take the S as the subject. Then, your negative two will become a positive two when you move it to that side. |
| 00:05:33 | Then 28 plus two T. It equals to three S. Divide the three from that side. That will look better. |
| 00:05:39 | It will look better if you divide three from that side. There will be no signs. |
| 00:05:43 | Then, substitute it to the formula number one above. Yep, don't move the S, move the T instead. |
| 00:05:50 | When you move the T to here, it will become positive. Yep. Divided by three. Erase this sentence and do it once again. |
| 00:07:16 | Number 19 should be okay. Is the answer correct? |
| 00:07:19 | I think it is okay. |
| 00:07:23 | Number 20. |
| 00:07:36 | The things that I taught yesterday were quite good. All of you seem to be getting it. |
| 00:07:42 | The whole equation is multiplied by three. Be careful when you are multiplying and do not miss any terms, or else, it will be wrong. Three times three... |
| 00:08:09 | Is the answer correct? No problems, right? |
| 00:08:15 | Do you want to do any of the problems? Or do you want me to talk about any of them? |
| 00:08:21 | Any questions? |
| 00:08:22 | If not, I will- this method- this will be it for the method of substitution for now. We will start to learn another method. Let's turn to the next page. Who will clean up the blackboard? |
| 00:08:41 | Turn to the next page. Eleven point three. Method of elimination [ in English ]. |
| 00:09:22 | Elimination in Chinese is elimination. [ in Chinese ] |
| 00:09:29 | Elimination. Elimination. To eliminate something. |
| 00:09:36 | Well, um... I will not talk about example number four in the book right now. I will talk about another one that is simpler, one that I have mentioned before. I have mentioned it before. |
| 00:09:46 | Um, do you remember I mentioned before- in the last two classes- that you should have learned it- seen it in primary school. |
| 00:09:53 | Um, it involves a big and a small number and you don't know what the numbers are. |
| 00:09:56 | The sum of the big number is, for example, 20. No, the sum of the big and small numbers is 20. |
| 00:10:04 | Um, the difference between the big and small numbers is, for example, eight. |
| 00:10:08 | Then, you are asked to find out the big and the small numbers. Do you remember? |
| 00:10:12 | At that time I said that you, um, after learning this chapter, |
| 00:10:15 | you will understand why your primary school teacher told you to find the big number by adding the sum to the difference and divide it by two. |
| 00:10:21 | To find the small number, you subtract the difference from the sum and divide it by two. The main point is that these are related to what I will be teaching right now. |
| 00:10:27 | Okay, I will be using this example to teach. This is not included in the examples of your textbook. However, this is simpler. |
| 00:10:33 | Suppose I have, um, a sample question here. You can copy it down in the book, um, in your notebook or textbook. |
| 00:10:40 | Solve A plus B is equal to 20. A minus B is equal to eight. Like that. |
| 00:10:48 | Well, now there are two numbers, A and B. The sum of these two numbers is 20 and their difference is eight. Is that right? It is obvious for you to see which is bigger and smaller. |
| 00:11:00 | Can you see it? Which one is bigger and which one is smaller? |
| 00:11:01 | A. |
| 00:11:02 | Uh, Ho Wai Kwan? |
| 00:11:05 | A. |
| 00:11:06 | A is bigger because the second equation- in the lower equation, A minus B is equal to eight. Therefore, A should be bigger than B. |
| 00:11:10 | Okay, I named the first equation as one and the second as two. Give them names. Well, we are not going to use the earlier method- the method of substitution right now. |
| 00:11:22 | The method of elimination is- um, like it is named, is to decrease the number of unknowns- to decrease the number of unknowns- to eliminate the unknowns. |
| 00:11:33 | In fact, this is closely related to the previous method, um, the main point that I was talking about earlier. |
| 00:11:38 | Didn't I mention before that, um, when there are two unknowns in a question, it is impossible to calculate it, right? |
| 00:11:44 | Well, do you remember from the previous- the previous method of substitution, you were trying to simplify two equations with two unknowns into one equation with one unknown. |
| 00:11:56 | Is that right? |
| 00:11:57 | Well, you can do it. In fact, the present method is using the same technique, too. |
| 00:12:03 | It is also trying to create an equation with only one unknown. Okay? But the question is, how do we do that? |
| 00:12:11 | The problem is how we put the two equations together. Okay, now, here is equation one and equation two. Well, you- you can see that here is two A. |
| 00:12:22 | Positive A here and here. Positive B here and negative B here. Right? |
| 00:12:27 | Okay, if now I want to find out A but B is blocking the way, right? So, what should I take away? |
| 00:12:39 | (inaudible) |
| 00:12:41 | The best is to take B away, right? Take away B and the remaining A will be easier to calculate, right? |
| 00:12:45 | The problem is how do we take A away? No, sorry, how do we take away B? |
| 00:12:48 | How to take away B? Okay, let's see. B is a plus sign here and a minus sign here. We have to pay attention to the plus and minus. Let me write them in color. |
| 00:13:00 | Okay, it's plus and minus. A plus and A minus. In this case, let's think that there are a positive B and a negative B. If you have to eliminate it... |
| 00:13:09 | If you have to eliminate it, you will add the two numbers together to eliminate it. Why? What is the sum of three plus negative three? |
| 00:13:15 | Zero. |
| 00:13:18 | Kam Mo Lam? |
| 00:13:20 | (inaudible) |
| 00:13:21 | Louder. |
| 00:13:22 | Zero. |
| 00:13:23 | Louder. |
| 00:13:24 | Zero. |
| 00:13:25 | Yes, zero, right? Right. Four minus- four plus negative four is equal to zero, right? So, now, positive B plus negative B is equal to what? |
| 00:13:32 | Zero. |
| 00:13:33 | Should it be zero? If it is zero then there is no B, right? Therefore, I will add these two equations together. |
| 00:13:39 | Okay, how do we add these two equations together? Adding two numbers is possible, but how do we add two equations together? We add equation one into equation two. |
| 00:13:49 | How do we add it? Here are two equations. There is an equal sign- equal sign in each equation. Add the left side of the equal sign to the left side of the other equal sign. |
| 00:13:56 | Add the right side of the equal sign to the right side of the other equal sign. Okay? So, 20 plus what? |
| 00:14:02 | Eight. |
| 00:14:03 | Twenty plus eight, right? Well, on this side, 20 plus eight is equal to 28. Okay? Okay, here, this one is added into this one. What is equal to A plus A? |
| 00:14:12 | Two A. |
| 00:14:13 | A plus A is? |
| 00:14:14 | Two A. |
| 00:14:15 | Two A, right? Well, but- I said earlier that positive B plus negative B is how many? |
| 00:14:19 | Zero. |
| 00:14:20 | Siu Hiu Ching. |
| 00:14:22 | Stand up. You should be accustomed to it. |
| 00:14:26 | Zero. |
| 00:14:27 | Right. Positive B plus negative B equals to zero, right? Do we need to write zero out? |
| 00:14:29 | No. If you want to write it out, write positive B and negative B out. It should be understood, right? |
| 00:14:33 | Well, you can see in this situation that what is left after the summation is? |
| 00:14:37 | Two A equals to 28. |
| 00:14:39 | What is the remaining unknown? |
| 00:14:41 | A. |
| 00:14:42 | A, right? Is there a B? No, it's gone. In this process we have eliminated the B. Do you understand? |
| 00:14:50 | This process has eliminated the B. That is, to eliminate B, okay? This method is called elimination. Okay? |
| 00:15:04 | Well, now that, um, B is eliminated, we can immediately find out A. A is... |
| 00:15:09 | Fourteen. |
| 00:15:10 | Fourteen, right? Okay? |
| 00:15:11 | So, you will realize the reason why when we are looking for the bigger number- A is the bigger number, right? We have said earlier that it is the bigger number. |
| 00:15:18 | When it is the bigger number, we need to add the sum to the difference- this is the sum and this is the difference- the sum added to the difference, is this right? What is the next step? |
| 00:15:26 | The sum added to the difference and then... divided by two, right? Can you see that? That will turn out like this. Can you see that? Get it yet? |
| 00:15:33 | Okay, next, how do we get the smaller number? |
| 00:15:40 | We have already found one of the unknowns. |
| 00:15:41 | Substitute it back into the equation. |
| 00:15:42 | Right, substitute it back into the equation, right? So, fourteen will be substituted back into the equation. It is up to you to substitute it into either equation. |
| 00:15:48 | Put A equals 14 into this, um, either one of the equations. Um, let's say equation two. Well, 14 minus B is equal to eight. B is equal to... |
| 00:16:06 | B:00] |
| 00:16:11 | Any questions? |
| 00:16:13 | B:00] |
| 00:16:27 | Okay? |
| 00:16:45 | Here I used- I added- I used summation. The B is eliminated when I used summation. Okay? |
| 00:16:52 | You may ask- you may say what if I want to eliminate the A? What should I do? What should I do to eliminate A? |
| 00:16:59 | Instead of eliminating B, I want to eliminate A first. Then what should I do? |
| 00:17:02 | Maybe I should teach you by using example number four in the textbook. Okay? |
| 00:17:10 | The student on duty, please clean up the blackboard. |
| 00:17:22 | Erase it. Erase it. |
| 00:17:42 | Example number four in the textbook. |
| 00:17:43 | Can I go wash my hands? |
| 00:17:44 | Go. Go. |
| 00:18:05 | I have taken role already. |
| 00:18:06 | Thanks. |
| 00:18:14 | Now the equation this time is similar to the one I have previously stated. One of them is A plus B and the other one is A minus B, right? |
| 00:18:20 | Now, it is three X plus two Y and three X minus two Y, right? |
| 00:18:24 | Just now, I eliminated the B- to eliminate B. So, now... if I eliminate the two Y- is there a plus and minus before Y? Is that right? |
| 00:18:37 | So, I should- based on the method I have mentioned before, I should add the two equations together. |
| 00:18:43 | When they are added together, positive Y and negative Y will become...? Will become zero, right? |
| 00:18:49 | Okay? Well, if- I said earlier that if I don't want to cancel this one- to eliminate this one, but rather, I want to eliminate this one- this one written in yellow- I want to eliminate this. |
| 00:18:58 | What should I do? |
| 00:19:02 | This time, I don't want to find out X first. I want to find out Y first. If I want to solve Y, I will need to eliminate X. I will need to... |
| 00:19:11 | Come in. |
| 00:19:12 | I need to eliminate X first. So, in order to catch your attention, I have purposely written it in yellow. |
| 00:19:18 | Well, how do we do the elimination? Pay attention. In the previous question, one is plus and one minus. In that case we add them together. |
| 00:19:25 | However, are this three X and this three X positive? Okay, what do you do when you cancel the X? |
| 00:19:33 | Subtract. |
| 00:19:34 | Three X and three X. How do we do it? |
| 00:19:36 | Move three X... |
| 00:19:37 | Move three X to the other side. |
| 00:19:38 | Cheng Ka Ho, what do you think we should do to eliminate X? Do you- do you have any ideas? |
| 00:19:45 | Three X minus three X. |
| 00:19:46 | Three X minus three X will be zero. Subtraction. So we- that is correct. It will work out by subtracting the two equations from each other. |
| 00:19:58 | Now, when you are doing the subtraction- this is easy- 19 minus 11 is equal to what? Eight, right? Right? |
| 00:20:04 | Well, what about here? Three X minus three X will be nothing- it will become zero, right? |
| 00:20:09 | Now, pay attention. Will it be zero if this is subtracted from this? This one minus this one. Will it become zero? |
| 00:20:14 | No, this one is plus and this one is minus. The two are different. One is plus two Y and the other is minus two Y. |
| 00:20:19 | So, if you really subtract them from each other, it will become two Y minus negative two Y, right? You should take- take the whole positive two Y minus two negative Y, right? |
| 00:20:28 | You will find out that after the subtraction is- here, negative times negative is positive- it becomes four Y is equal to eight. Therefore, Y is equal to... two. Okay? |
| 00:20:37 | So, pay attention to this. This will be mistaken easily- you will get this wrong easily. Therefore, put Y equals two into... either one of the equations, um, let's say... equation one. |
| 00:20:52 | So, three X plus two, then times two equals 19. Three X is equal to- move four to the other side is equal to 15. X is equal to five. Therefore, the solution... |
| 00:21:10 | X equals five. Y equals two. Okay? |
| 00:21:17 | Any questions? |
| 00:21:21 | Any questions? |
| 00:21:26 | So, you can see that- in concluding the two methods- two- two, um, methods- these two examples that I have done. At the first time, I add the two equations together. |
| 00:21:35 | At the second time, I subtract the two equations. It all depends on which unknown we want to eliminate. Okay? Let's say we want to eliminate Y- in fact, I can eliminate Y now. |
| 00:21:47 | So we can add them together since one is positive and the other is negative. |
| 00:21:51 | If both of them are positive numbers and we want to eliminate the X. In that case, we use the two- the two equations by subtracting each other. Okay? |
| 00:22:03 | In fact, you can control it yourself- which one you want to calculate- which one to calculate first. Okay? Any questions? Well, it is now your chance to try it out. |
| 00:22:13 | Open your class workbook. Turn to... |
| 00:22:21 | Exercise 11 B. Page 119. Well, try out number one to four. |
| 00:22:27 | [ Bell ] |
| 00:22:28 | One to four first. |
| 00:22:32 | Check the answers when you are done. |
| 00:23:57 | You have to circle- to circle equation one and equation two or else it will be confused as numbers one and two, right? |
| 00:24:22 | Chan Lap Man, come up and do question number two. |
| 00:24:26 | Did you hear? |
| 00:24:27 | Number two. |
| 00:24:28 | After you have finished. |
| 00:24:57 | Hey. |
| 00:24:58 | Yes? |
| 00:24:59 | You haven't given it a name. |
| 00:25:00 | Oh, yeah, that's right. |
| 00:26:34 | Chan Lap Man, hurry up. |
| 00:26:56 | Question number three (inaudible). |
| 00:26:57 | Come up and do question number three later. |
| 00:27:02 | (inaudible) |
| 00:27:03 | Yes? |
| 00:27:05 | (inaudible) X is (inaudible). |
| 00:27:06 | Name equation one and equation two first. |
| 00:27:14 | Yep. |
| 00:27:15 | You have to tell me which equation minus that equation first. How do you work this out? Two X is equal to 12. |
| 00:27:20 | Addition. |
| 00:27:21 | Addition. In that case, write one plus two. Equation one plus equation two. Right. Colon. |
| 00:27:29 | Next, um, it is equal to six. Substitute X is equal to six back into the equation. |
| 00:27:33 | This X is equal to six, so... it becomes six minus Y is 10... |
| 00:27:42 | So, you move six to here and why can't you subtract them? Y can be a negative number, right? Can Y be negative four? |
| 00:27:49 | Um, that is right. |
| 00:27:53 | Can I erase this? |
| 00:27:55 | Erase it. Erase it. Erase it. |
| 00:27:58 | Erase the ones I wrote on the top too. |
| 00:28:03 | Erase the ones I wrote on the top too. |
| 00:28:05 | Erase example four too. |
| 00:28:55 | Chan Lap Man, it is a colon after your equation one minus equation two- it's a colon, don't write it like an equal sign. |
| 00:29:03 | Conversely, your equal sign is like a colon. Write the equal sign in a better way. |
| 00:29:37 | Question number two is correct. Pretty well done. However there are some places that are not well written- written- written. Not clearly written. |
| 00:29:44 | What is that thing down there? Is that a one- one under the (inaudible)? |
| 00:29:48 | X equals to one. |
| 00:29:49 | No. Here. Why is it- here- here, what is this? |
| 00:29:53 | Nothing. |
| 00:29:54 | You did not write that? |
| 00:30:04 | Ten A equals 30. |
| 00:30:12 | Three... |
| 00:30:22 | Any questions? |
| 00:30:26 | Are all four questions completed? |
| 00:30:28 | (inaudible) |
| 00:30:34 | Check your answers with the ones on the blackboard. Both of them are correct. Pretty good. |
| 00:31:11 | Here. Of course you cannot find the answer by adding the two equations together. What do you expect to be eliminated by adding the two equations together? X plus X is two X. |
| 00:31:20 | Six Y plus two Y is eight Y. You cannot cancel them. With six Y and two Y, no matter whether you use addition or subtraction, you cannot cancel it. |
| 00:31:27 | Look, six Y plus two Y is eight Y and subtraction will leave four Y. The Y will still be there. |
| 00:31:34 | On the other hand, there are two X. Both X are positive. |
| 00:31:37 | If you use subtraction, the X will be cancelled. Therefore, you should never use addition- addition to calculate this question. |
| 00:31:44 | If you use addition, nothing will be cancelled- nothing will be eliminated. If and only if you use subtraction, then you will make it. |
| 00:31:51 | Right? Do not mindlessly use addition all the time. |
| 00:31:53 | You have to see if anything will be cancelled, right? Here, it is for sure that only X will be cancelled, right? |
| 00:32:09 | Finished? Raise your hand if you have not finished. Raise your hand if you have not finished. |
| 00:32:18 | Raise hand. |
| 00:32:19 | (inaudible) |
| 00:32:29 | Take a look at the example if you have finished. Example five. |
| 00:32:51 | Student on duty, clean up the blackboard. |
| 00:32:55 | (inaudible) |
| 00:32:56 | No, the upper one times the lower one. |
| 00:32:58 | (inaudible) |
| 00:32:59 | Are there any questions? |
| 00:33:00 | The one on the bottom... |
| 00:33:02 | Are there any questions? |
| 00:33:14 | Finished yet? |
| 00:33:20 | Why are you so slow? |
| 00:33:30 | Hey, why are you lying on the table? |
| 00:33:35 | Finished? |
| 00:34:13 | I will not wait for you due to the time constraint. Stop for a moment. Calculating number four- for those of you who have not finished, are you doing number four? |
| 00:34:22 | I am doing number five. |
| 00:34:23 | Stop for a moment. Please take a look at example five. Page 117. Page 117. |
| 00:34:32 | Now, this equation- this question is slightly different from the previous ones. |
| 00:34:38 | It is because, you will find out that when you add the two equations together. Two X plus X is three X. It cannot be eliminate- eliminated- cannot eliminate the X. |
| 00:34:51 | This one plus this one will leave a Y here. Three Y plus negative two Y, right? The biggest question is that this is a three but that is not a three, right. |
| 00:35:00 | This is a two but that is not a two. |
| 00:35:01 | This is a two but that is a one, right. If you subtract the two equations, the unknown will not be cancelled. |
| 00:35:10 | When this is the case- which is quite common- of course, you can ask me whether you can use the previous method of substitution. Of course you can. |
| 00:35:19 | However, we are learning the method of elimination now. So, if we have to use the method of elimination in this case, how do we do it? |
| 00:35:26 | Here, the biggest question is that this is two, this is one, this is three and this is two. They are all different, right? |
| 00:35:33 | If they were the same number, we could find some ways to use addition or subtraction to eliminate, is that right? Is there any way to make them the same? |
| 00:35:39 | Multiplication. |
| 00:35:40 | I said it yesterday. What I said yesterday is mainly for today's lesson. |
| 00:35:44 | What we learned yesterday can be- of course- used to solve mathematical problems, but today we can use it too. |
| 00:35:50 | If the numbers are not the same, we can think of some ways to make them bigger, right? For example, if I want to eliminate the X but this is two and this is one. |
| 00:36:00 | If I turn the one into two, then, both of them will be two, right? In another words, if I turn this into two, we have multiplied it by two. Therefore, the rest of the equation will be...? |
| 00:36:09 | Multiplied by two. |
| 00:36:10 | Multiplied by two. Okay? So, I need to solve equation number two first. Multiplied it by two first. Okay? |
| 00:36:18 | Equation two times two. After multiplied by two, the first part will be two X and what about the second part? Chan Kwan Wu, after multiplied by two- after multiplied by two...? |
| 00:36:29 | The second part... uh, positive four Y. |
| 00:36:34 | Four Y and then? |
| 00:36:36 | Twenty-four. |
| 00:36:37 | Twenty-four, right. Okay? Now, we have formed a new equation, right? Let me give it a name. Equation number three. Okay? |
| 00:36:43 | So, now, I will not look at equation number two anymore. |
| 00:36:45 | Since it is turned into equation number three, okay? So this is two X and that is two X too. What do we do next? |
| 00:36:51 | Lo Pak Man. Should we use addition or subtraction for the two equations? |
| 00:36:59 | Addition or subtraction? |
| 00:37:02 | Subtraction. |
| 00:37:03 | Positive two X and positive two X. |
| 00:37:05 | If you want elimination, shouldn't we use subtraction? Use subtraction, okay? Two X minus two X is...? |
| 00:37:06 | [ Bell ] |
| 00:37:15 | Zero. |
| 00:37:16 | It became zero. Two X minus two X is zero, okay? If you add them together, what will it be? Two X plus two X is what? |
| 00:37:20 | (inaudible) |
| 00:37:21 | Four X. In that case, the X will not be cancelled. Understand? Since both of them are positive, you will need to use subtraction. Sit down. |
| 00:37:27 | So, we use this- equation one minus equation three. We will no longer use equation two. |
| 00:37:33 | Equation one minus equation three. This one minus this one. After that, two X minus two X will be zero. |
| 00:37:40 | So, three Y- positive three Y and this is negative four Y. Subtraction. Three Y minus negative four Y, okay? This is negative four Y and that is positive three Y. |
| 00:37:53 | Equals to three minus 24. Three minus 24 looks really strange. It is a negative number, but it is okay to have a negative number. Three minus 24. |
| 00:38:01 | So, let it be three minus 24. Well, next, this will become seven Y, right? How about this one? |
| 00:38:09 | How many? |
| 00:38:10 | Negative 21. |
| 00:38:11 | Negative 21. |
| 00:38:12 | Negative 21, right? So, Y is equal to... |
| 00:38:13 | Negative three. |
| 00:38:14 | Negative three, okay? Next, put Y equals negative three into any one of the equations above. |
| 00:38:20 | I will not suggest you putting it into equation three, because it had been multiplied. |
| 00:38:24 | It is more complicated. So, I will put it into equation one or equation two. Put it into equation two, okay? |
| 00:38:29 | So, X minus two times negative three equals 12, okay? So, X is- this is six and move it to the other side, it becomes six. Okay? |
| 00:38:45 | Negative two times negative three equals positive six. Move the six to the other side, it becomes negative six. Six. |
| 00:38:49 | So, the solution... |
| 00:38:52 | B:00] |
| 00:38:56 | Y equals... what is Y equal to? Negative three, right. Okay? Any questions? Now, the most important point is- I think- this step here. |
| 00:39:08 | How do we use the method of elimination? In the process of elimination- before that, we may need to multiply some, um equation. |
| 00:39:17 | By doing that, we will make both numbers of the equations the same. |
| 00:39:20 | This one multiplied by two will become two and that one is two. So, they can be subtracted by each other, okay? |
| 00:39:24 | If you say, if I want to eliminate the Y- earlier I said I want to eliminate the X but if I want to eliminate the Y, one is three and the other is two, what should I do? |
| 00:39:34 | Chong Fong Wai. If I want to eliminate the Y, I will need to make them the same. So how do we make three and two the same? |
| 00:39:43 | Find out their LCM. |
| 00:39:44 | Find out their LCM. The LCM of three and two is...? |
| 00:39:48 | Six. So, three times what is six? |
| 00:39:50 | Two. |
| 00:39:51 | Times two. If three time two, then, the whole equation- equation one will need to be multiplied by two. Okay? How about this one? Two times what? |
| 00:39:57 | Three. |
| 00:39:58 | Two times three. It is six again. Okay? So, we need to multiply the lower equation by three, okay? Understand? |
| 00:40:02 | If you want to eliminate the Y, you will need to do more things. |
| 00:40:06 | If you multiply the upper equation by two and the lower equation by three, that will create equation three and equation four. Equation three and equation four. |
| 00:40:12 | Then, we can add the two equations together. One is positive six Y and one is negative six Y, okay? Understand? |
| 00:40:19 | Try it out at home. Since we only have one class today, (inaudible). |
| 00:40:24 | Well, um, go back and try out number five to eight. Okay? Go back and do number five to eight. Okay? That is not too many. |
| 00:40:35 | It should be the day after tomorrow- do we have class on the day after tomorrow? Day six. We have class on day six, right? |
| 00:40:41 | Okay, we will talk about it more on day six, because we will have a test tomorrow. Do you remember? |
| 00:40:44 | What? |
| 00:40:45 | (inaudible) |
| 00:40:46 | Test. The chapter on slopes. |
| 00:40:47 | Day five, right? Distance formula. The chapter on slopes. Any impressions? |
| 00:40:49 | Slope? |
| 00:40:53 | No. |
| 00:40:55 | This equation. |
| 00:40:58 | Parallel. Straight. I have just talked about it. |
| 00:41:00 | B:00] |
| 00:41:02 | There is also the distance formula. A B equals- the distance between two coordinates. |
| 00:41:07 | B:00] |
| 00:41:11 | Tomorrow- tomorrow, you will be tested on chapter eight. It seems like all of you have amnesia. |
| 00:41:21 | Tomorrow- um, are there any single lined papers? |
| 00:41:24 | No. |
| 00:41:31 | Who is in charge of buying the papers? |
| 00:41:34 | (inaudible) |
| 00:41:35 | It is you? Chan Lap Man? Help me buy one more pile of F four- long paper, single lined, white colored, tomorrow. Long paper. |
| 00:41:44 | Is the test going to be difficult? |
| 00:41:45 | Not difficult. Study for the test. Stand up. |
| 00:41:48 | Do we need to bring our books? |
| 00:41:50 | You don't need to bring books tomorrow, okay? However, do you remember you have to bring two new books tomorrow? |
| 00:41:54 | I remember. |
| 00:41:55 | (inaudible) |
| 00:41:56 | Yes |
| 00:41:57 | Okay. |
| 00:41:59 | (inaudible) |
| 00:42:02 | Goodbye class. |
| 00:42:03 | E:00] |
| 00:42:11 | (inaudible) |
| 00:42:12 | Sit down and be quiet. The student on duty, come up and clean up the blackboard.
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