Remember, a letter simply represents a number in algebra.
Sometimes this may be set but sometimes it is up to you to work out what the number is worth.
Where a number can change it is called a variable.
In this activity, all of the answers must be whole numbers or zero.
x + 3y = 8
What do we know? That the total must be 8.
What is set and what can't be changed? The answer is set and that y needs to be multiplied by 3.
What are we in control of? Why are these variables? x and y are the variables because they could be several different numbers.
Through trial and error, we can find options:
The three different combinations can be shown in a bar model
Option 1: If x is 2, then 3y must be 6 so that they add up to 8. If 3y is 6, then y is 2.
Option 2: If x is 5, then 3y must be 3 so that they add up to 8. If 3y is 3, then y is 1.
Option 3: If x is 8, then y must be 0 so that they add up to 8.
Let's have a look at the questions now.