# Equation with Two Variables: How Many Answers? (1)

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

Key stage:  KS 2

Curriculum topic:   Algebra

Curriculum subtopic:   Use Variables

Difficulty level:

### 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.

Look at this equation:

a + b = 8

The two numbers, a and b, must add to 8.

They 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 7.

If a is 2, b must be 6 etc....

The results can be shown in a table:

a   b
0 8
1 7
2 6
3 5
4 4
5 3
6 2
7 1
8 0

There are 9 solutions.

Look at this equation:

a + b = 2

Match the answers for b to the answers for a, to give the correct solutions.

## Column B

a = 0
b = 2
a = 1
b = 0
a = 2
b = 1

Look at this equation:

a + b = 2

How many solutions does it have where a and b are whole numbers or zero?

Look at this equation:

a + b = 3

Match the answers for b to the answers for a, to give the correct solutions.

## Column B

a = 0
b = 0
a = 1
b = 3
a = 2
b = 1
a = 3
b = 2

Look at this equation:

a + b = 3

How many solutions does it have where a and b are whole numbers or zero?

Look at this equation:

a + b = 4

Match the answers for b to the answers for a, to give the correct solutions.

## Column B

a = 0
b = 2
a = 1
b = 0
a = 2
b = 3
a = 3
b = 1
a = 4
b = 4

Look at this equation:

a + b = 4

How many solutions does it have where a and b are whole numbers or zero?

Look at this equation:

a + b = 5

Match the answers for b to the answers for a, to give the correct solutions.

## Column B

a = 0
b = 0
a = 1
b = 3
a = 2
b = 4
a = 3
b = 2
a = 4
b = 1
a = 5
b = 5

Look at this equation:

a + b = 5

How many solutions does it have where a and b are whole numbers or zero?

Look at this equation:

a + b = 7

How many solutions does it have where a and b are whole numbers or zero?

Look at this equation:

a + b = 10

How many solutions does it have where a and b are whole numbers or zero?

• Question 1

Look at this equation:

a + b = 2

Match the answers for b to the answers for a, to give the correct solutions.

## Column B

a = 0
b = 2
a = 1
b = 1
a = 2
b = 0
EDDIE SAYS
0 + 2 = 2
1 + 1 = 2
2 + 0 = 2
• Question 2

Look at this equation:

a + b = 2

How many solutions does it have where a and b are whole numbers or zero?

3
EDDIE SAYS
0 + 2 = 2
1 + 1 = 2
2 + 0 = 2
• Question 3

Look at this equation:

a + b = 3

Match the answers for b to the answers for a, to give the correct solutions.

## Column B

a = 0
b = 3
a = 1
b = 2
a = 2
b = 1
a = 3
b = 0
EDDIE SAYS
0 + 3 = 3
1 + 2 = 3
2 + 1 = 3
3 + 0 = 3
• Question 4

Look at this equation:

a + b = 3

How many solutions does it have where a and b are whole numbers or zero?

4
EDDIE SAYS
0 + 3 = 3
1 + 2 = 3
2 + 1 = 3
3 + 0 = 3
• Question 5

Look at this equation:

a + b = 4

Match the answers for b to the answers for a, to give the correct solutions.

## Column B

a = 0
b = 4
a = 1
b = 3
a = 2
b = 2
a = 3
b = 1
a = 4
b = 0
EDDIE SAYS
0 + 4 = 4
1 + 3 = 4
2 + 2 = 4
3 + 1 = 4
4 + 0 = 4
• Question 6

Look at this equation:

a + b = 4

How many solutions does it have where a and b are whole numbers or zero?

5
EDDIE SAYS
0 + 4 = 4
1 + 3 = 4
2 + 2 = 4
3 + 1 = 4
4 + 0 = 4
• Question 7

Look at this equation:

a + b = 5

Match the answers for b to the answers for a, to give the correct solutions.

## Column B

a = 0
b = 5
a = 1
b = 4
a = 2
b = 3
a = 3
b = 2
a = 4
b = 1
a = 5
b = 0
EDDIE SAYS
0 + 5 = 5
1 + 4 = 5
2 + 3 = 5
3 + 2 = 5
4 + 1 = 5
5 + 0 = 5
• Question 8

Look at this equation:

a + b = 5

How many solutions does it have where a and b are whole numbers or zero?

6
EDDIE SAYS
0 + 5 = 5
1 + 4 = 5
2 + 3 = 5
3 + 2 = 5
4 + 1 = 5
5 + 0 = 5
• Question 9

Look at this equation:

a + b = 7

How many solutions does it have where a and b are whole numbers or zero?

8
EDDIE SAYS
0 + 7 = 7
1 + 6 = 7
2 + 5 = 7
3 + 4 = 7
4 + 3 = 7
5 + 2 = 7
6 + 1 = 7
7 + 0 = 7
• Question 10

Look at this equation:

a + b = 10

How many solutions does it have where a and b are whole numbers or zero?

11
EDDIE SAYS
0 + 10 = 10
1 + 9 = 10
2 + 8 = 10
3 + 7 = 10
4 + 6 = 10
5 + 5 = 10
6 + 4 = 10
7 + 3 = 10
8 + 2 = 10
9 + 1 = 10
10 + 0 = 10
---- OR ----

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