Use substitution to find the possible values of two variables

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In this lesson you will learn how to use algebra to write and solve equations that contain two missing numbers.

This lesson includes

  • two videos
  • two worksheets

Created in partnership with Pearson


The examples in the videos are often easy enough to solve with just a few notes, but we will use algebra to find the solution so we can practise the method.

This problem, and all the problems in this lesson have more than one solution. Our thinking will be about finding lots of solutions, then deciding which solutions make sense in the context of the problem.

We will use algebra to support the problem-solving method, but you might be able to find your own methods for solving these problems too.

We will use substitution to work out possible answers and think about why some answers aren’t possible in the context of the question.

In this video we’ll use a real-life problem as our context. Can you spot the solutions that make sense, and the ones that do not? How can you be sure you have found all the solutions?


Activity 1

These activities will develop your thinking about solving equations and choosing solutions that make sense in the context of the problem.

In questions 3 a and b, how can you record and organise your solutions to be sure you have found them all?

Algebra worksheet

Activity 2

Practise solving problems that have more than one solution in a range of contexts.

In question 1, can you draw a bar model that represents the problem? Or, is there a different model that helps you to organise your thinking?

Solving equations worksheet

Click here for the answer sheet for both worksheets.

There’s more to learn

Have a look at these other resources around the BBC and the web.

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