In this activity, all the answers will be whole positive numbers or zero.

 

An equation with two variables involves two numbers which must be found.

 

"I think of two numbers.

When I double the first and add this to the second, I get 8."

 

 

In written algebra, when a and b stand for two numbers, we can change the problem above into this:

 

2a + b = 8

 

This means that twice a added to b must come to 8.

a and b are whole positive numbers or zero.

 

What could they be?

 

If a is 0, b must be 8

If a is 1, b must be 8 - 2 = 6

If a is 2, b must be 8 - 4 = 4

If a is 3, b must be 8 - 6 = 2

If a is 4, b must be 8 - 8 = 0

 

The results can be shown in a table:

 

a	b
0	8
1	6
2	4
3	2
4	0

 

There are five solutions.

 

Shall we have a go at this in some questions now?