Examples of what pupils should know and be able to do
Solve simultaneous linear equations such as:
5x + y = 17
5x – y = 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?
- FTM(S)Y789 p127 -129 - Acrobat pdf document (56Kb)
- 1999 test P1 Q9 (L7) - Microsoft word document (56Kb)
- 2001 test P2 Q16 (L7) - Microsoft word document (32Kb)
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 5x –
y = 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
–5x – y = –17 etc