Solving Simultaneous Equations using Elimination and Substitution Method

Okay. right now I'll be presenting this question that is that taught my student yesterday regards to the elimination method for simultaneous equation. So without further ado, let me go right to this question. Okay, this question there are two equations. You have over 4. Okay, let me just rewrite the question here. You have over 4 - 3 / 8 = 3. Okay, probably you're thinking you're intimidated by the fraction. So what you can do is to multiply by 8 throughout this whole expression because 8 is the LCM of 4 and 8. So if you to multiply by okay this is multiply this not this multiply multiply by 8. Okay, you multiply by 8, you have / 4 * 8 - 3 / 8 * 8 = to 3 * 8. All right, every term multiply by 8. So you think for one moment when you multiply by 8, the four and the eight you can cancel off. Four become one, eight become two. This become 2x then the 8 you can cancel off this become 3 and 3 * 8 is 24. So this is your equation one. Okay. Then after that your equation two apparently is your 5x / 3 - / 2 = 12. So this whole equation you multiply by six because six is the LCM of three and two. So if you to multiply by six okay the whole equation you multiply by six and that is what we have. So this one your six and your three can cancel off. 6 will become 2. 2 * 5 is 10 6 and the 2 can cancel off this become 3 6 * 12 is 72 so now have my two equation equation one and equation two okay because the question want you to do by elimination right so you can see right now both equation one and equation two they have -3 so since both have the same -3 you can minus one from the other. So I'll minus equation one from equation two. Okay, the reason is because right 10 - 2x eventually you end up with positive number of That's the reason why you use equation 2 minus equation one. So you can write it this way. 10 - 3 This is your equation 2 and minus your equation one. Then equation two minus your equation one. Okay. Then after that you open the bracket. So when you open the bracket you be careful of your negative sign. Okay. This will become -2x - 72 - 24 you can ask your good friend calculator you'll get 48. Then after that your 3 - 3 + 3 your 3 automatically been eliminated. Am right? So 10 - 2x is 8x 8 is 48. Therefore will be 6. How about your Okay, is six. You substitute into any of the equation. Okay, let's choose equation one. So if to substitute = 6 into equation 1, you end up with 2x 2x - 3 = 24. And if you will continue to solve this equation. Okay, let me probably just scroll down. okay. Let me just bring this thing up so that space. Okay, bring it up so have space. Okay, let's focus on your this part. Okay, when your is 6. Okay, 2x - 3 is 24. 2 * 6 is 12. 12 - 3 = 24. Okay, then after that this is your -3 right? So, let's say leave my -3 here. Then 24 12 here is positive, right? bring to the right side will be 24 - 12. 24 - 12 is 12. So -3 is 12. So = -4 because 12 / -3 is -4. So you solve for this question. = 6 and = -4. Okay. hope this is clear on how to do this question. Okay. And then let's move on to the next question. Okay, this is also by elimination. Okay, let me quickly show you how to do this question. So you have - 3 over 5 is equal to - 7 / 2. Okay, for this kind of equation, right, because you have fraction equal to another fraction. So what do you do? You think for one moment. So what told you yesterday, you cross multiply. Okay, that's how you cross multiply. Then after that, this is your 2x - 6 = 5 - 35. Then after that your 2x will then be equal to 5 minus how many? 30 - 35 + 6. What do you have? -35 you add 6 you have - 29. Your -6 bring over become positive 6. So you have 2x = 5 - 29. And this is your equation one. Okay. Then after that 11x = 13 If is if 11 = to 13 22x will then be equal to 26 Okay, this one 2x is 5 - 29. Right? Because you want to do by elimination. Am right? So equation one you multiply by 11. Why multiply by 11? because want to create 22x down here. So you have 2x * 11 equal to 11 * 5 - 29. Okay? Because you equation one you multiply by 11 you have this because want to create 22x. Yes. So that can carry out my elimination. That's the reason why you multiply by 11. Then this one multiply by 11. have 55 - 29 * 11. 29 * 11 what do you have? You have 31 9. Okay. It's okay to deal with bigger number because you no need to deal with fraction. So so you can decide what you want. You want to deal with fraction or deal with bigger number. Okay. From experience it's always better dealing with bigger number than dealing with fraction. Yeah. That's the reason why advocate this way of solving equation. But if you prefer to deal with fraction, can show you how to do it using fractional way after this part. So after that, you have your equation two and equation three, right? Okay. Because your equation two has 22x and equation three has also 22x. Therefore, you can use equation 3 minus equation two. Okay? If use equation 3 minus equation 2, you think for one moment 22x - 22x, you get zero. Correct? Then 55 - 26 what do you have? 55 - 26 you have 29 Okay, 55 equation three minus equation two, right? So you have 55 - 26 you have 29 then -319 there's nothing to minus right because there's no numbers for equation two am right? So you write -319 down here. Then the -319 you bring to the left side of the equation. You will have 319 equal to 29 So your 29 = 319. So your is equal to 319 / by 29. So 319ide by 29. You end up with 11. So that is your How about your Okay, your 11 is 13 So 11x is equal to 13 because is 11. So if 11 is 13 So you think for one moment 11 * is 13 * 11. So if were to cancel off my 11, divide by 11 on left and right, you have = 13. Okay, that's the reason why equal to 13. So this method is lot faster compared to using the fraction method. So now show you keep the fraction what do how how to do. Okay, this is what usually what school will teach. So - 3 over 5 = - 7 / 2. Okay, school sometimes they may not teach you cross multiply. Sometime they would I'm not sure about your school but this one right if were to continue let's say have to keep my fraction around right you I'm going to let this be - 3 over minus - 7 / 2 = 0 then after that combine it into one fraction right so this one will become 10 the denominator make it 10 okay because LCM of five and two is 10. So how did five become 10? multiply by two. So numerator also multiply by two. Since denominator multiply by two. Then after that how the two become 10? multiply by 5. Okay. Then after that you have 2x 2 - 3 2 * 3 is 6 over 10 - 5 - 5 * 7 35 / 10 = 0. Then after that you would have 2x - 6 minus 5 + 35 over 10 = zero. You combine into one fraction negative negative is positive. Okay. Then after that 2x - 5 - + 29 over 10 = 0. Okay. Then after that you have 2x will then be equal to 5 - 29 because the 10 bring over 10 * 0 is nothing. Right? So left with numerator. Then bring min - 5 and 29 to the right side. So - 5 become positive 5 positive 29 become negative - 29. Okay. Then this is your equation one. All right. Then equation two is your 11x = 13 Okay. Then you just continue to do what did earlier. You get the same answer. Okay. This is probably what your school teaches you. Okay. Let's move on to the next question. Okay, the next part is your use by substitution method. So how do you actually substitute? Okay, this one is show write the question here first. So you have over + / 2 = 4. Okay, I'm going to show you my method which show you yesterday. Okay, first multiply by six throughout. So if multiply by six, why six? Because six is the LCM of 2 and three. So four also need to multiply by six because I'm multiplying by 6 throughout. All right. Then after that this will become 2x + 3 = to 24. Okay. Then you don't deal with fraction anymore. Then after that this equation you have 2x over 3 - / 6 = 1. Same thing multiply by six throughout. Okay, multiply by six throughout. Then you end up with 4x - = 6. Okay. Then after that they want you to do by what? Substitution. Am right? Okay. They want you to do by substitution. Then this will become 2x = 24 - 3 and substitution you taught you yesterday right you no need to make the subject you can actually create 4x here because instead of substituting can substitute 4x instead of you you get what mean so multiply by two okay multiply by 2. So have 4x = 48 - 60 - 6 So now can substitute 4x 4x = 48 - 6 into equation one. So substitute into equation one. Instead of writing 4x change it to 48 - 6 and minus again = to 6. So have 48 - 7 = 6. Okay - 7 can bring to the right side. Right? Become 7 Six can bring back here right so -6 so this is 42 is 7 then can rewrite as 7 is 42 so = 6 okay now you know = 6 you can substitute into any of the equation all right will suggest this equation here this equation here because that is your 2x so 2x is equal to 24 - 3 because your is 6. So this will become 24 - 18. 3 * 6 is 18 and this is your 2x. So your 2x will then be equal to 6 and is equal to 3. Okay. So this is my method and how saw do it using substitution. So what your school teaches right is this method. Okay. Your school will show you this method. over 3 + / 2 = 4. Okay. Then after that what they would do is they they make over 3 the subject 4 - / 2 then the whole thing times three. Right. Okay. Okay. Okay, they make subject. This is your Then after that, this is your equation two. Then they substitute equal to this into your equation two. Correct? That's by substitution. So they substitute Okay, this is equation one. So substitute = 3 bracket 4 - / 2 into equation two. Then you end up with very complex fraction. Okay, that is what your school will show you most of the time. So 2x your Okay, your is this guy. Okay, 2x. This is your 2x. Your is 3 bracket 4 - / 2. 2x over 3 - / 6 = 1. Okay, then you solve this equation. So this equation it it looks lot more intimidating to solve to be honest compared to the one show you. But this one right you can actually apparently can cancel off the tree here. Okay. then you don't need to worry about the bigger fraction. Then you can rewrite this as two bracket 4 - / 2 - / 6 = 1. Okay. Okay, but that's not all. Then after that they'll expand this. This will become 8 minus 2 multiply this in right is 8 - then - / 6 = 1. Then after that you you have 8 - 1 = + / 6. Then this is 7. So + over 6. This is your 6 / 6 + / 6. Okay? Because is 6 / 6. Okay? Because the six can cancel off become right? so this 6 over 6. Why? Why 6 over 6? Because the denominator is 6 here. Okay? Then after that 6 + is 7 / 6. 7. Then 7 is equal to 42 because the six bring over 7 * 6 42. 7 remain here right so = 6 okay is six but that's not all you need to find your also so then is this right so substitute = 6 so will then be equal to 3 bracket 4 - is 6 right 6 / 2 then you just solve for okay 3 bracket 4 - 6 / 2 is 3 then 4 - 3 is 1 so is drink. Okay. So, this is how likely what your school show you in in using stick to the algebra way and and the initial part especially here would be very confusing because of the kind of you substitute in. So, you see which method works for you. personally prefer non-fraction method so that it's lot easier to do although you're dealing with bigger numbers. So, it depends on your own preference. you prefer to deal with algebra or mean you prefer to deal with fraction or or bigger number. Okay, leave it to you. Should show you two methods? Okay, then the last question. Same thing by substitution again. Okay, by substitution. Okay, I'm going to show you my methodology also. So this one is three. The equation one will be 3x - = 23. because you have your place here nicely for you, right? So you make the subject. So this one will become 3x equal to + 23 because shift my to the right side of the equation. Then the 23 shift to the left side, right? Because want to make the subject. This will be 3x minus 23. Okay? So your is actually 3x - 23. that is your Okay. Now you have your in place. You can substitute into this equation, right? Let's call this equation two. And this is your equation one. So equation two you have over 3. substitute. So substitute = 3x - 23 into equation 2. Okay, when you substitute what do you do? is mean your so your your remain right is over 3 and what is your Your is 3X - 23. Okay, your is 3X - 23. So instead of writing change my to 3x - 23. Okay, so over 4 = to 4. All right, then after that what do you do? Your school will teach you to make these two denominator the same. Right? But my method is multiply everything by trough. So see which method you prefer. Okay? Maybe show you your school method first. Then show you my method. Okay? This is your school method. Your school method will teach you this one. Change it to 12. Denominator change to 12. But if my denominator change to 12, please do nothing with the number here. Okay, because you are not multiplying by 12 throughout at the moment. You are just changing the denominator to 12. So three change to 12. multiply by four. So numerator also multiply by four since denominator multiply by four. So same thing how the four become trough? You multiply by three, right? So numerator also multiply by three since denominator multiply by three. So if multiply by 3 have 9 instead of 3x. So 23 * 3 have 6 to 9. Okay, hope this is clear. Then after that you combine into one fraction, right? 4x + 9x - 69 / 12 = 4. Okay. Then 4x + 9x what do you have? 9 + 4 is 13x. So this is 13x - 69. Okay. Over 12 = to 4, right? but the 12 bring over to the right side. 4 * 12 is 48. Okay. Then you have 13x is equal to 48 + 69. Okay. This part here is just simplify this part. get this as my numerator. Then originally you should have over trough, right? But the over trough bring over to the right side multiply by trough. So trough bring over is four multiply by trough. that's why get 48. Okay. Then 48 + 69 you have 117. So 13x is 117. So is equal to 117ide by 13 you have 9. So is 9. is equal to 3 bracket 3x - 23. Okay, is 3x - 23. So is 9, right? So substitute is 9. So you have 27 - 23, you have four. Okay? So this is your school method. All right? Then now quickly show you my method. Okay? the method suggest to you see which way you prefer. So once you reach here right so what what what do you do you get rid of the fraction am right so how do you get rid of the fraction you multiply by trough throughout so if multiply by trough okay this is what you have okay I'll write out the full equation here mean the full working here okay multiply by 12 throughout so this one the three and the 12 can cancel off right this is 4x 4 and the 12 can cancel off right so 3 * 3x - 23 have 9x - 69 = 48 okay then after that have 13x = 48 + 69 you have 117 as well is equal to 117 / by Then you have 9. Then you substitute is 9 is equal to 4. Okay? So hope this is clear. So see which way you prefer. All right? So show you your school way and also my way. See which way you prefer, which way you understand better. You can always replay this video as many times as you want and you can watch it slowly. So hope this video helps you. So wish you all the best. Okay. So that's all for now. Thanks you for watching my video. Thank you. Bye-bye. All the best.