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Equation with Two Variables: How Many Answers? (2)

In this worksheet, students must find how many integer solutions there are to a given equation with two variables.

'Equation with Two Variables: How Many Answers? (2)' worksheet

Key stage:  KS 2

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   Equations and Algebra

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

In this worksheet, all the answers must 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."

 

Written using algebra, where a and b stand for my two numbers, we get:

 

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 5 solutions.

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