Practise Solving Simple Equations With More Than One Possible Answer

In a previous activity, we found the possible values represented by letters, when all the letters stood for positive whole numbers or zero.

 

We looked at two basic types.

 

p + q = 4

Where the possible pairs of numbers were:

p = 0 when q = 4

p = 1 when q = 3

p = 2 when q = 2

p = 3 when q = 1

p = 4 when q = 0

 

That is two numbers whose sum is 4.

 

pq = 8

 Where the possible pairs of numbers were:

 p = 8 when q = 1

 p = 4 when q = 2

 p = 2 when q = 4

p = 1 when q = 8

 

That is two numbers whose product is 8.

 

                                     

In this activity, we are going to do a little work before we can identify the pairs of numbers. 

 

 

Let's see what they will look like!

 

Example

 

 

 Find all the possible values represented by a and b, when they stand for positive whole numbers or zero.

 

Answer

First, we need to know what the sum of a and b are, so we just want a and b on their own.

To get rid of +6 we can -6 from both sides.

 

 

 

Which now equals

               

 

Much easier to deal with now!

 

Possible pairs of numbers with a sum of 3 can now be listed.

 

a = 0 when b = 3

a = 1 when b = 2

a = 2 when b = 1

a = 3 when b = 0

 

Let's try some questions - come on!