00:00 Hello, I'm Sonday Oyase, I'm your mathematics teacher, but today, and now we're taking

00:20 an important topic, which is change of the subject of formula, especially substitution.

00:26 So let's go change of subject of formula, okay?

00:48 So I'm talking about change of the formula at the end of this topic, what are you expected

01:03 to know?

01:04 As expected to know how to change the subject of the formula, how to identify a particular

01:09 formula and what to do with it.

01:13 So we'll move straight.

01:14 The first question I would like to ask is, what is change of the subject of formula?

01:20 Every equation is expressed in a variable.

01:24 So it's a variable which is expressed in terms of all that variable in a formula.

01:30 So that means a variable stands alone, whether on the right hand side or on the left hand

01:35 side, and it's an expression of every other variable.

01:40 So if every other tenel goes on the right hand side or the left hand side, but one variable

01:46 stands alone.

01:47 So it stands alone as a variable.

01:49 So the variable that stands alone is called the subject of the entire formula.

01:54 Now let's go ahead, I give an example, let me have a variable where I have V equal to

02:02 U plus U plus A, C. Now I have a combination of many variables here, so I have V, U, A, and

02:20 C.

02:21 Now these variables are involved.

02:22 But one is an expression of every other variable, that's the V.

02:27 So the V, A, is the subject of this entire formula, so the V stands alone.

02:36 So even if the V is at the right hand side or the left hand side, it becomes the subject

02:41 of this entire formula, that.

02:44 The problem comes is when I'm trying to change this V to U, A, or T, that process of

02:54 changing is called the change of the subject of formula.

02:59 First, the subject of the formula, then a change.

03:03 Now if I'm trying to change, that means I am substituting it for any other variable.

03:09 That's when substitution comes.

03:10 So substitution comes when you are trying to change a particular subject from any other

03:16 one that you have before, to anyone.

03:18 So substitution comes like that.

03:20 So we substitute the value of U, A, and T, as you may have it, to any of the subjects.

03:27 So once I'm doing that, it's a change of the sort of formula.

03:31 Now, let's go.

03:32 Now, changing of the sort of formula is a change of the subject that begins with the variable

03:36 to become a new subject and apply the inverse operation for the solving of the equation

03:42 in the opposite order for the convention.

03:45 But I'm just saying that you're changing any of these to replace this, that's change of

03:51 the subject.

03:52 Now the question lies is, how do I go about it?

03:55 Let's pick, for example, I want to make, this is the V already at the subject of the formula

04:01 to really identify from what is given.

04:03 So I can be given any other equation, but take a note of what's whereby it is given

04:09 at the subject.

04:10 So changing it would not be difficult, but if you don't identify the previous subject,

04:15 into a new subject can be so difficult.

04:18 So let's go.

04:19 We have V.

04:20 Now, I want to now make what, U, the subject of this entire formula, what do I need to do?

04:27 I have multiple variables running.

04:29 I have V, I have A, I have T. Now, to change the dynamics behind it, I look for the proximity

04:37 developed at this closer to U, then the one far away.

04:42 So I have A and T, closer, I have V, V, I have to stick across the equation sign.

04:47 So that's a bit longer, but I have the ones that are closer, I have A and I have T.

04:53 So making U, yeah, the subject of the formula, what do I need to do?

04:58 I have to figure out four eliminates A and T, and how do I do that?

05:03 To eliminate A and T, A and T have a coefficient that they go with.

05:07 The coefficient is an additional sign, this is the coefficient, this, the plus becomes

05:16 very important.

05:17 Because if I don't take note of this, it's a set whatsoever a position I do.

05:21 So what do I need to do?

05:22 Take note of this plus, that the sign of equality.

05:26 Now, when I take note of this plus, let me now continue.

05:29 So I will now have a variable where I have V equal to U, I have Z equal to U plus A and

05:46 T. Now, subtract minus A, T, the inverse of plus A, T, so if I want to do that, what do

05:58 I do?

05:59 Now, subtract, I want to subtract it, I need to subtract this, apply it to the both side

06:05 of the equation on the left hand side and on the right hand side.

06:09 How do I make that possible?

06:10 Now, that means that the inverse of a plus becomes a minus, the inverse of a minus becomes

06:17 plus, the variable stands alone, but I take note of the coefficient.

06:22 So what do I have?

06:23 And I have applied to both side, I'm going to be having V inverse of it minus, what's

06:31 the variable I'm eliminating, A and T. So I'm eliminating A and T of the grid.

06:39 So I'm having A, T equal to U plus A, T minus A, T.

06:50 Put the inverse, subtract it from both sides, you take the inverse and subtract from both sides.

06:54 So I'm taking the inverse of the addition sign, it gives me minus, so I'm minus, but variable,

07:02 so I could have, yeah, taking off this out of the equation.

07:08 Oh, I would have plus, A, T minus A, T. So, and taking it out, this takes out this.

07:25 I'm left with the U. So practically, the U becomes a new subject.

07:30 So I want to have it as V minus A, T equal to U. U, right hand side on the left hand side

07:42 becomes the subject.

07:44 Now the previous subject is V, the new subject is U. The process in between is what you do

07:53 to get your view.

07:55 So a member could have, what I said on this side, so I would have U equal to V minus A, T,

08:04 categorically.

08:05 So I have a new subject in place.

08:08 Now moving to the next one, let's have another example.

08:14 So it's okay.

08:15 Let's have another example where we could use T using the same form of equation, the same

08:19 equation with being given. Let's have example 2.

08:24 Stay given the same form of equation, you can say we call we have V equal to U plus A, T.

08:36 Now the one we got is making U the subject of the formula.

08:41 Now we are expected to make C the subject of the formula.

08:45 This becomes a bit more difficult than the previous one.

08:49 The previous one is, you just have to eliminate one.

08:52 But yeah, you have multiple variables to deal with.

08:54 So you look for the closet of them, what's the closet?

08:57 The closet to T, it's A. First, the nest is U. You don't start.

09:05 You look at that the closet.

09:06 Now the A is the closet, then the U followed by the U. But while doing this, take note.

09:12 Start from the one at the simpler, 12 minutes.

09:14 So I have a U here.

09:16 So I can take off this U out of this equation because U here is plus U. The sign, there's

09:22 always a sign in front, so I can take off the U. So what do I have to do, subtract U from

09:27 both sides.

09:28 So I just subtract U from both sides.

09:29 Now let's go.

09:30 So I can simply say a solution to that, for example, take subtract U from both sides.

09:36 Now when you are subtracting U, you are not only subtracting the U, you are subtracting

09:41 what do we call, the sign, inverse of the sign.

09:44 This is plus U.

09:45 So we are subtracting U from both sides.

09:47 So I'll be able to know what minus U. So I will have V minus U equal to plus U plus A T minus

10:00 U. Now if you take note of this very well, if you following carefully, you'll see why

10:09 am I bringing this minus U. So it could eliminate this effectively.

10:14 Take off this U plus and minus.

10:17 So what do I have left, my total equation, my total equation gives me V minus U equal

10:24 to A T.

10:28 Now when I have it this way, it's much more easier now to identify that from this equation,

10:37 this one that I have now, I'm still looking for T, but I have A and T. So A and T is not

10:46 a subject.

10:47 T is what I want to be the subject.

10:49 So what do I do?

10:50 I divide both sides by anything in front of T. What's in front of T, A?

10:57 So divide both sides. So simply say I divide both sides and divide both sides by A or divide

11:09 both sides by A. So when I take out divide both sides by A, what am I left with?

11:19 So what I have, V minus U over A equal to A T divided by A, taking the addition.

11:34 So this goes this. So what do I have left in my system of equation?

11:41 And I have V, I have a V minus U over A equal to T, beautiful.

11:55 You know, this beautiful.

11:57 Now T is the new subject. What do I mean?

12:01 I have V, I now meet T the subject. So when I turn the right side, like I said, on the left

12:07 side, in the other side it is. This is not a new subject. Taking everybody in supportive

12:14 position. So if you, what are you moving to the other side too, I could not, you cannot

12:19 have it as T equal to V minus U over A, good. Now if you look at it, this and this are

12:32 the same. It's all. So I have option.

12:36 So if I have a particular option and I'm giving like this, I'm giving this form, they are

12:40 the same. It's on the right hand side, on the left hand side, it is still the subject

12:44 of the formula because it stands alone. So we'll move to another example, a bit tough

12:52 one. Now we have example three. This one is made quite the subject of the formula from

12:57 the equation. So the question is, yeah, we have multiple variables. I have X, Y, Z. Now,

13:04 what do I need to do? Like I said, take the one closer. Then I have example three. The

13:12 equation, example three. I have X equal to open bracket Y plus Z, Y plus Z. Then I have,

13:29 I have Y minus Z. Now, whichever I have, yeah, take note of it. But here I have RBA, it's

13:39 a subject to this one here. This X here becomes the whole thing that this thing's been expressed

13:47 with. So you cannot mention this without mention this first. So when you are mentioning,

13:52 you say, okay, X equal to, you can't say Y plus Z. It has to start with X. So that means

13:57 X becomes the subject in this entire one. Now we are saying, change it and make what?

14:02 Now make what? Why? To become the solution formula. What do you do? First of all, you take

14:08 a pause. I have Y here. I have another Y down here. I have two. What do I need to do? So, if

14:15 I were you, the first thing to do is this. I will just simply say a solution. Now, what

14:22 do I put in place? O, I'm a challenge. I have X. So what do I need to do? I have X over

14:29 1, express it in a fraction, equal to Y plus Z over Y minus Z. Now, why am I making this?

14:43 I want both to be on the same side. The numerator, the denominator, I want to create both sides.

14:49 So what do I need to do? I put it this way. Now, I have two ways to grab out it. I could

14:55 add up this over 1, then multiply both sides by this, this, this, this, it's on two positions.

15:02 So I have two positions. I could add up multiply both sides by this or take out this. It's optional

15:07 for me to do. But this, I pay this with one. So I will just want multiply both sides by

15:12 what? Why am I not so? Let's go. So what do I need to do next? Next, I will cross multiply

15:19 or multiply both sides. We may have it. I will have X. I will have X. Open bracket Z minus

15:28 Y minus Z equal to Y plus Z. Cut to go again. Y plus Z. So this way. Now, with this, what

15:43 am I done? I just cross multiply or multiply both sides by minus Z minus Y. I have two options.

15:50 So it will be two options. Still, it comes back to this. So giving you a two option line.

15:55 Oh, that is, what? So I have, when I do this, I have this. Now, I need to open the bracket

16:00 because this is multiplying this. So X multiplies everything in the bracket. So what do we have?

16:05 X opens the bracket. What do we have? X times Y becomes what? Becomes X Y minus X times

16:14 Z becomes X X Z X and Z. And I have on this side, Y plus Z. So the question now, let's

16:31 see. What do I do next? I have Y. I have another Y here. I have two Ys. What do I need to do?

16:37 I need to collect light ends. The terms of Y here, I have another Y here. Bring them together

16:44 to become one family. Why? Every other one that does not belong to the family, cross

16:50 over to the other side. So what do I need to do? So categorically, collect light ends.

16:56 So simply say, collect light ends. Collect light ends. Now, collect my light ends. If I'm

17:06 collecting my light ends, what do I need to do in this point? I collect the ones that have

17:12 similar light ends, the ones that are similar in nature. So I have X Y. And I have, yeah,

17:21 I have plus Y. It causes the sign of equality or it takes two sign plus Y. I want to eliminate

17:30 the Y here so it could be on this side. So what do I do? I collect my light ends and how

17:36 do I collect my light ends? I could send these to cause the sign of equality. Or in the

17:42 other way, I could multiply. I could just simply say, why can't I divide both sides by

17:46 minus Y? So I have two options. So what do I do? I have X plus Y. Take this. I have this

17:54 cross. It becomes what? Minus Y equal to Z. This cross becomes plus X plus XZ. XZ. Now I have

18:08 X and Z. Categorically. What have I done? What have I done? I've been able to take out the

18:17 ones I know and group them into the category that belong. Good. Now, looking at this. Looking

18:27 for me. For me, I collect my light ends. And when I collect my light ends, I have X Y minus

18:35 Y equal to Z plus XZ. Now, if we look at it carefully, between the two sides, what's

18:44 common? And between the A, what's common? So between these two sides, you observe, I have

18:51 Y to be common. Between the A, too, I have Z to be common. So the Z on one side, the Y on

18:58 the other side. So between the A, I have what's common? Y. So I take out the Y. Now, taking

19:03 out the Y, I will have Y, open bracket X minus Y into Y. That's one. Close the bracket

19:15 equal to Z is common. Take it out. I take out the Z, open bracket, what? One plus plus

19:30 X. Close the bracket. So, what do I do here? What have I just done? I have collected the light

19:39 ends of both sides. Now, it returns back. I have Y. After a little minutes, what's the

19:46 base in front of Y? I want the front of Y, I have X minus 1. So with X minus 1, divide

19:51 both sides. Divide both sides by X minus 1. Now, it divide both sides by X minus 1. So,

19:59 I will just simply say divide both sides by X minus 1. Now, divide both sides by X minus

20:14 1. Now, when I divide both sides by X minus 1, what do I have left? So let's take out the

20:19 equation together. I have Y, open bracket X minus 1, all divided by X minus 1 equal to Z,

20:31 open bracket X, 1 plus X, over, we have X minus 1. Now, if you are following the system

20:47 pattern of the equation, you would definitely observe that I am having X on both sides.

20:55 Now, I am not bothered with the X because X is not what my subject wants to be. My subject

21:01 remains. I am looking for a pattern to make Y. So, I simply take this in this. So, when

21:07 I take out this too, what do I have left? I have Y, Y equal to Z, open bracket 1 plus X,

21:23 over X, I have 1 plus X over X minus 1. Now, as I said, this process is a bit more complex

21:44 than the first, the second and the third. So, if you look at it very well, I now have Y

21:50 here equal to all the system of equation. Previously, in the system, I have X, but now I have

21:59 been able to change the X to Y. The process in between is the process I have undertaken

22:06 to change the X to Y. Now, I take the last one more question is make Q, the sum of the formula.

22:15 So, I have four questions, a bit more, make Q. Now, this one becomes make Q, that is example

22:25 4, that is example 4. Now, make Q, what my system of equation? I have X equal to A, Q,

22:37 square. Now, I am introducing square, someone said, oh, but those ones we are not square

22:43 yes, you could have a system of equation, you could have square, you could have square root,

22:49 you could have Q, you could have Q, so you get your mind prepared for it. Oh, from simple,

22:56 simple. So, this X here is the subject, the one that was given, I am changing this X to

23:03 Y to Q, all my first steps, solution. Now, I take say, a solution to the question, solution

23:13 and how, what do I eliminate first? What do I eliminate first? Is that the square or the

23:22 A? Because those two things I want into my head, what do I eliminate first? The first

23:26 eliminate is A. You say, why? If I take out the square, the square will have fed the A,

23:34 the square will have fed both sides. I can decide, I can take out, let me take out the

23:37 A first. So, I only have the Q and the two to deal with. Closer, you won't prove, let

23:45 me take a said. So, divide both sides by A. So, I am dividing both sides by A, a divide

23:55 both sides by A. So, I divide both sides by A. So, I divide both sides by A, I will have

24:07 X over A equal to A Q square over A. So, conveniently, means, conveniently, I could

24:22 just take out my E. A out of the equation, wherever A is, A is on the side. But yeah, I am

24:32 trying to get my Q. So, I will just have, I will have, I have X over A equal to Q square.

24:44 Now, with the Q square, with the Q square, Q square is subject, but what the subject should

24:51 be is Q. So, what the next thing to do? I have square. To take away square, you square root.

24:59 To take away square root, you square. Opposite. To take away square, you square root. To take

25:05 away square root, you square. So, to take away this square, I square root both sides. So,

25:11 how do I, let me go on with the system of equation? I want to square root, square root

25:16 both sides. It has to apply to both sides. Square root both sides. So, I have square root

25:20 both sides. So, when I want to square root both sides, both sides. Now, less square

25:28 both sides. So, when I square root both sides, I am going to be having square root X over

25:34 A equal to Q square square root. It has to apply to both sides. So, that this one takes

25:44 out this effectively. And so, what do I have left? I am now going to be having what? I am

25:51 now going to be having a square root X over A equal to Q. Now, Q is now the subject of

26:03 the formula. Now, with this, we start from A down to the next one to the next to the next

26:11 and now this. So, you could also pick it to this side and take it to this side. In another

26:15 side, you decide to put it. There is no problem. So, we can move now. You have to do something

26:22 for me. So, you pick up your pen and your paper and solve the system of equation for me.

26:30 So, I have met P, the subject of the formula. I have X P equal to 4C minus Y. Ask question

26:39 1, question 2, make out the subject of the formula. Your final answer from the example 4, we

26:48 have Q equal to the root X over A. That is your final answer. So, you are going to be taking

26:58 some evaluation on. So, you are going to be doing some work. You are going to make P, the

27:03 subject of the formula for the first system of equation. You are going to make out and say

27:08 the formula for the second system of equation. So, you have two evaluation to work on and

27:14 that was 20 new intelligence. Thank you very much. You have come to the end of the class.

27:18 I still remain, or yes, someday. Thank you very much. See you in the next class.