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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.

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

Key stage:  KS 2

Year:  Year 4 11+ worksheets

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   Equations and Algebra

Difficulty level:  

Worksheet Overview

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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