The cost of 1 protractor is 30 pence. If I spent £2.70, how many did I buy?

A compass costs 50 pence. 8 protractors and 3 compasses costs £8.70. What is the cost of a protractor?

1 compass and 1 protractor costs £1.10. 2 compasses and 1 protractor costs £1.60. What is the cost of a compass?

If 10 compasses and 3 protractors cost £4.20. 10 compasses and 6 protractors cost £5.40. Find the cost of 1 protractor.

If 10 compasses and 3 protractors cost £4.20. 10 compasses and 6 protractors cost £5.40. Find the cost of 1 compass.

Finding two unknowns from simultaneous equations.

﻿Hi, , this is Ms. Bridgett and in this lesson, we're going to be looking at writing simultaneous equations algebraically. Make sure you've got a pen and some paper and take a moment to remove any distractions. Okay, let's make a start. I'm going to show you some information in a moment and I'd like you to read through it and think very carefully about what's the same and what's different about it. So here are the first two sets of information, here are the second two sets of information. Read through them, think what's the same and what's different. Pause the video now. Okay, here are some of the things that you might have come up with. So some of the information is written in words. Some of the information is written algebraically. Some of the information contains the same numbers. So on the left, we've got a seven, a two, and a 4.36. And on the right, we've got a 0.5, a two, and a 4.50. Now, I don't know if you've noticed what's stayed the same and what's different about those worded scenarios. Now, they're both about buying stationery. They're both about somebody going along and buying some stationery and we're told some information about the total cost that they spent. There is, however, something slightly different about them and not just the items that they bought. In the first scenario, we're told that Carla buys seven protractors, but we're not told the cost of the protractors. If we look on the right-hand side, Zaki's information, we're told the pens cost 50p, but we're not told how many he buys. So there's something quite different about those. So on the left, we've got the number, but not the cost, and on the right, we've got the cost, but not the number. What we're going to move on to next is how those words relate to their algebra. The information about Carla and what she bought and how much she spent has been translated into the equation underneath the words. The same thing has happened with the information about Zaki. It's been translated into an algebraic equation, which you can see underneath. Now in those equations, we've got unknowns. In the equation on the left, you can see p and you can see an r, they are the unknowns. In the equation on the right, we can see p and we can see c. Now, an unknown in an equation might represent the cost of an item, it might represent the number of items, it might represent something else completely. What I would like you to do is to think about what those unknowns in each of those equations represent. Look at the original scenario they came from and what do those unknowns represent? The second thing that I'd like you to think about is p. Now the p appears in the equation on the left, there is also a p in the equation on the right. Does it represent the same thing in both of those equations? Pause the video and have a think about it. Okay, let's look at the equation on the left that came from the information about Carla. We've got seven p plus two r equals 4.36. Now, we know that she buys seven protractors. So that p represents the cost for the protractor. We know that she buys two rulers, so that r represents the cost of the ruler. We move on to the equation on the right. Again, we're given the information about how much is actually spent, but this time we're told that a pen costs 50p. So here, the p represents the number of pens that he bought. We're told that a calculator costs two pounds, so here c represents the number of calculators that he bought. That two c represents the total cost of the calculators, that 0.5p represents the total cost of the pens. Now, p does not mean the same thing in both of those equations. So in the equation on the left, I used p to represent the cost of a protractor. On the right-hand side, I used p to represent the number of pens. It doesn't represent the same thing. What I'd like to do, finally, on this slide is have a think about if we have enough information to work out the value of p, r, and c. Pause the video now and have a think about it. Okay, I know that we do not have enough information to work out p, r, and c. So we do have two equations and we do have some unknowns, but those equations are not related to one another. It's not a system of equations. They're not simultaneous equations because the scenario on the left has got absolutely nothing to do with this scenario on the right. There is nothing in common about them at all to do with the unknowns and the amount that was spent. We have no information to be able to work out any of those unknowns. In a moment, I'm going to show you some words and some expressions, and I'd like you to match the words to their corresponding expressions. Now, to help you out along the way, I'm going to tell you a little bit more information about the scenario they're describing. So in this scenario, Yasmin is buying some stationery. She's buying protractors and she's buying rulers. Protractors cost two pounds, rulers cost one pound 50. Yasmin's buying p protractors, and she's buying r rulers. Now be careful, because not everything has got a match. So here are the expressions. Here's the information in words. Pause the video and have a try. Okay, let's have a look at the answers to these. So we'll start at the top and move down. The total amount Yasmin spent, she spent money on protractors, she spent money on rulers. She spent two pounds on each of those protractors and she's bought p of them. And she spent one pound 50 on rulers and she's bought r of them. So the total amount that Yasmin spent is represented by this expression here, two multiplied by p plus 1.5 multiplied by r. Now, if we dive into that a little bit more and just think about the total cost of the protractors, remember, we know the protractors cost two pounds, we know that she bought p of them, so the total cost of the protractors is going to be the cost multiplied by the number of items, that's going to be two p. Let's think about the number of items that Yasmin bought. She bought protractors. She bought rulers. She bought p protractors and she bought r rulers. So the total number of items that she bought is the number of protractors plus the number of rulers, p plus r. Finally, the total cost of the rulers. We know that each one costs one pound 50. We know that she's bought r of them. So to get the total cost, we're going to multiply those two things together, 1.5 multiplied by r. For your final task of this lesson, I would like you to see if you can come up with a different scenario to match this pair of simultaneous equations. So our unknowns are x and y. We know that x plus y is equal to 12. And we know that four x plus two y is equal to 30. So can you come up with a worded scenario that could describe that? Remember, because these are simultaneous equations, the scenarios have got to relate to one another. So whatever x represents in the first equation, it has to represent the same thing in the second equation. Try to make your example as varied or as interesting as possible. Pause the video now and have a try. Okay, I'm going to share with you the example that I did. So, because everything we've done so far has been about cost or number of items bought, I wanted to do something slightly different. So I'm going to tell you that I've got some rabbits and chickens, and I'm going to tell you that the amount of rabbits and chickens I've got is 12. The next thing that I'm going to tell you is that the number of legs there are is 30. So how this relates to the equations is the x represents the number of rabbits and y represent the number of chickens. So altogether, I've got 12 animals. Now, in the next set of information, I've got four x, four times the number of rabbits. Rabbits have got four legs. Two y represent the number of chicken legs all together. So each chicken has got two legs. There are y chickens, two y. Now, I would love for you to be able to take a photo of the equations that you came up with and to send them to your teacher and share them with your teacher. If you'd also like to, you can ask your parent or carer, and you can send a picture of your equations to @OakNational on Twitter and that way I'd be able to see some of them too. Thank you for your time today and all of your hard work and I will see you in the next lesson, when we start looking at solving algebraic, simultaneous equations.

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)?

Let p be the cost of a protractor. If I buy 3 protractors, which of the following represents the total cost?

Let p be the number of protractors bought and q be the number of rulers bought. Protractors cost 20 pence and rulers cost 15 pence each. What does 15q represent?

Let p be the number of protractors bought and q be the number of rulers bought. Protractors cost 20 pence and rulers cost 15 pence each. What does p+q represent?

Let p be the number of protractors bought and q be the number of rulers bought. Protractors cost 20 pence and rulers cost 15 pence each. What does 20p+15q represent?

Writing simultaneous equations algebraically

In this lesson, we will learn to write word simultaneous equations algebraically. We will then interpret worded problems and write two algebraic equations based on the information provided, then solve them.

Maths

Y9 Maths

Key Stage 3

Year 9

Solving linear simultaneous equations algebraically

Algebra

THEME

UNIT

Reviewing solving equations

Equivalent equations

Linear relationships

Combining algebraic relationships

Exploring expressions with two variables

Exploring systems of equations

Solving simultaneous equations

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

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.

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?

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:Writing simultaneous equations algebraically

Core Content

Solving linear simultaneous equations algebraically: