In this lesson, students explore a set of two-variable linear equations, constructed so that when you solve any pair of them simultaneously you get solutions which are all non-negative integers.

After students have done this, their task is to construct their own set of 2, 3, 4 or more equations with the same property.

This generates lots of opportunity to practise solving simultaneous equations, while at the same time focusing their attention on how the process works and what they need to do to obtain integer solutions.

Why teach this?

Simultaneous equations are a powerful way of modelling situations in which there is more than one variable.

Key curriculum links

Solve two simultaneous equations in two variables algebraically.

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