Step 10 Objective

Solve a pair of simultaneous linear equations by eliminating one variable; link a graphical representation of an equation or pair of equations to the algebraic solution.

Examples of what pupils should know and be able to do

Solve simultaneous linear equations such as:
5x + y = 17
5xy = 3

x + 6y = 101
x + 3y = 56
In 5 years' time Ravi’s father will be twice as old as Ravi. In 13 years' time, the sum of their ages will be 100. How old is Ravi now?

Probing questions

What methods do you use when solving a pair of simultaneous linear equations?
What helps you to decide which method to use? Talk me through a couple of examples and explain why you chose the method you did.

Are there any other solutions to this pair of simultaneous equations? How do you know?

Is it possible for a pair of simultaneous equations to have two different solutions? How do you know?

How does a graphical representation help you to know more about the number of solutions?

What if pupils find this a barrier?

Ask pupils to find all the possible solutions for one of the linear equations, for example 5x + y = 17. Similarly ask pupils to find a range of solutions for a second linear equation, say 5xy = 3.
Explore what they notice.

Repeat for other pairs – then establish a link with graphical representation.

It may be necessary for pupils to convince themselves that multiplying produces an equivalent equation – so 5x + y = 17 is equivalent to:
10x + 2y = 34
15x + 3y = 51
–5xy = –17 etc