What is the purpose of solving an equation?

Which of the following can be values when solving equations?

What is the value of x for x - 4 = 3x + 2?

What number am I thinking of, if half of the sum of my number and 4 is the same as 3 lots of my number subtracted by 2?

The perimeters of the rectangle and triangle are the sane. What is their perimeter?

Reviewing Solving Equations Quiz

﻿Hi everyone, and welcome to our next lesson, all about equivalent equations. I'm Ms Jones, and I will be teaching about this today. And just before we start, make sure you have a pen and paper, make sure you've got rid of all your distractions, and that if you can try and find a nice quiet place to work. Pause the video to make sure you've got all of that ready to go. So the first thing that I would like you to do, is have a look at these four people and their statements. And tell me what is the same and what is different about each of those statements below. The first one says, I tripled my number, subtract 12 and get 11. The next one, I double my numbers, subtract 12 and get 11. The next one, I multiply my number by six, subtract 24 and get 22. And the final one, I quadruple my number, subtract 24 and get 22. Pause the video here to have a go what's the same and different about those. So hopefully you started to create some equations to help you answer this question. You might have noticed that for example, two have the same value of X, if you were to solve those equations. Two equal 11 on the right hand side, whereas two equal 22 on the right hand side. And I'm hoping that we started to potentially recognise that if you began to solve these, some of these actually have the same value of X. I will be talking about that and a little more detail in the next slide, but for now, hopefully you can see that this equation here is actually just all of it's being multiplied by two, to get this equation or this statement here. Similarly with this one has all been multiplied by two to get this one. And you'll notice that they have the same value of X, which is very interesting. We can use equivalent equations, to solve equations more efficiently. This could be seen in the previous activity where if we found one person's number, we could use equivalent equations to find another. So as we saw in the previous slide, one person said, I triple my number, subtract 12 and gets 11. So you've got three X subtract 12 equals 11. And if you were to solve that equation, you would eventually get X equals 23 over three, because you'd add 12 to both sides, which would get me three X equals 23, then divide both sides by three, so X would equal 23 over three. This one here, I multiply my number by six, subtract 24 and get 22. As I've said before, to get from this one to this one, multiplying everything by two. So we've almost got two lots of this equation here. two lots of three X subtract 12 and two lots of 11. Now we know from solving equations or whatever we do to one side, we can do it other. So if I was to divide this side two, I'd have to divide this by two. And I still have the same equality would balance. And I know they have the same value of X, actually, both of these have the same value of X. So this one has the value, 23 over three as well. And this isn't just the case for multiplying and dividing both sides by the same. It's also the case for addition and subtraction. So if we look at this one that wasn't on the previous slide, a triple my number, subtract nine and get 14. This one, can you see the link between this equation, and this original equation? Pause the video to try and have a think about what the link is, and tell me what the value of X is going to be. So hopefully you've noticed that to get from this equation, back to my original equation, I'm actually just subtracting both sides by three. And that gives me the same equation as we had before, which means the X value is going to be the same. These are all equivalent equations. And especially when we get more complicated equations, with lots of steps to find X, it's actually much quicker. If we recognise that they're equivalent to just use the X value that we've already worked out for another one. So what I would like you to do now is to pause the video, to complete your independent tasks, where you're looking at all of these equivalent equations and finding links between them. So your first task was to match the equivalent equations. Some of these were really straightforward and simple. Some of them are a little bit trickier. So this one, for example, they're just multiplying all of the values by two. So we know that that was equivalent because, we've just multiplied them by two, but this one, these are equivalent, but that one was slightly trickier to recognise, I think. And if we say, for example, multiply this one, all of it by two, hopefully then we can see a little bit more easily, why these two are equivalent. Because if I subtract one from this side, I'd be subtracting one from this side, and we get an equivalent equation. So this one similar, but this one that the first step I would do is just to multiply both sides by two. So they at least look a bit more similar. It's easy to recognise why these ones are equivalent. Hopefully then you can see just subtract two from both sides and that's why they are equivalent. So this second question, we're using that equivalents to find the value or to find the answer. So I've been told that 2.2 X subtract 7.5, equals eight over nine, and that is a fact. So the question is, what is 4.4 X subtract 15? Now I know that I've multiplied this by two to get here, so I've got to do the same to the other side, and that gets me 16 over nine. This just means or equivalent, so if you did a mixed number, or you simplified your function, as long as it has the same value and that's fine. And similarly for this one, this one, this side has to be multiplied by three over two, so this side does as well. The take a mine was multiplied by three quarters and then you add two thirds. So you do the same thing to the other side as well. So you can see how this equivalence can be used, to find answers quite quickly or to find related facts. Have this explore task. How many ways can you use the number cards, to make Zaki and Binh have equivalent equations. So we want to use this six cards. We want to use four of them, for different cards, to fit in these gaps to make these two people have equivalent equations. So for example, if I put two here, I need to think about what are the numbers, I can use to manipulate these and make them equivalent. So pause the video to have a go at that. And these could have been your answer. So if I just separate them like this, so if I put four here and I put two here, I would need to put six here and three here, this works because if I had get rid of this, if I had this equation to make it look more similar to this one, I'm going to be multiplying it by three, because I've got to get from two X to six X. So if I multiply this whole thing by three, I've got six X, add 12 equals 12, subtract six y. Six X and my six subtract six y are the same. And if I've got add three and three here, I've just added eight to nine, sorry to both of these, to get 12 on either side. So those two are equivalent. There's another example here. And there's lots of other examples that you could have suggested. So if you've got any examples, you want to check, send it to your class teacher, or you can share your work if you'd like to, but please ask your parent or carer to share your work on Twitter, tagging @OaKNationalnational and #LearnwithOak if you want to share your answers on Twitter. That's the end of today's lesson, amazing well done. This is really quite a complicated thing to understand, but once you've got it, it really helps you, to work up things a lot more quickly and efficiently. So really well done it, if you caught up with all of stuff.

What must an equation have?

Which equation is equivalent to 3x - 2 = 4?

Which equation is equivalent to 4x - 2 = 8?

Which equation is equivalent to 3x - 2.5 = 5?

If 9 - 2x = 4, what is 7 - 2x?

Equivalent Equations Quiz

In this lesson, we will explore equations and develop our ability to be able to idenitfy equivalent equations in a list.

Maths

Y9 Maths

Key Stage 3

Year 9

Miss

Equivalent equations

Solving linear simultaneous equations algebraically

Algebra

THEME

UNIT

Reviewing solving equations

Linear relationships

Combining algebraic relationships

Exploring expressions with two variables

Exploring systems of equations

Solving simultaneous equations

Writing simultaneous equations algebraically

Checking the solution of simultaneous equations

Solving a simultaneous equation algebraically

Eliminating a variable

Manipulating systems of equations

Solving word problems

Using substitution to solve simultaneous equations

Substitution or Elimination

Simultaneous equations by trial and error

Let p be the number of protractors bought. If each protractor costs £2, which of the following represents the total amount spent on protractors (in pounds)?

If x=2 and y=3, what is the value of 2x+3y?

Use substitution to decide which of the following is the solution to x+y=3 and 5y+3x=15.

Fill in the gaps: The "n" in the nth term represents the ____.

Which sequence is formed as a result of adding "4, 9, 14, 19, ..." and "12, 8, 4, 0, ..." together?

I want to buy 3 rulers and 3 protractors. If they cost 40 pence each, how much will I spend?

If p+1=6 and p+q+1=7, what is the value of q?

4x +8y=116 AND 4x +4y=68. Solve

Is there a solution with x value between 0 and 1?

Look at the picture below and then fill in the gap: If two equal expressions are both __________ by the same quantity, then the two resulting expressions will be equal.

3x+2y=5 AND 3x-2y=7.  If I add these two equations together, which unknown will be eliminated?

Lesson overview:Equivalent equations

Core Content

Solving linear simultaneous equations algebraically: