Equations: Solutions to Simple Equations with Two Unknowns

In this worksheet, students must find pairs of numbers that satisfy a simple equation with two unknowns.

Key stage:  KS 2

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   Equations and Algebra

Difficulty level:

QUESTION 1 of 10

In this worksheet, we look at equations with two unknowns.

a and b stand for two numbers, which could be different or the same.

Look at this equation.

a + b = 8

It tells you that a added to b is 8.

We are looking for any two numbers that add to 8 in order to satisfy (fit) the equation.

If a is 6, b will be 2.

If a = 2, b = 6.

If a = 9, b must be negative. b will be -1.

If a = 4½, b = 3½.

Example

a - b = 7

Which of these solutions satisfy the equation?

a = 7, b = 0

a = 0, b = 7

a = 10, b = 3

a = 10¾, b = 3¾

Put the given pairs into the equation to see if a - b is 7 or not.

 a = 7, b = 0 fits because 7 - 0 = 7 a = 0, b = 7 does not fit because 0 - 7 = -7 (not 7) a = 10, b = 3 fits because 10 - 3 = 7 a = 10¾, b = 3¾ fits because 10¾ - 3¾ = 7

a + b = 7

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 4, b = 3

a = 3, b = 4

a = 7, b = 7

a = 10, b = -3

a - b = 5

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 8, b = 3

a = 3, b = 8

a = 17, b = 12

a = 10½, b = 5½

b - a = 5

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 8, b = 3

a = 3, b = 8

a = 17, b = 12

a = ½, b = 5½

a + b = 12

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 4, b = 7

a = 8, b = 4

a = 7, b = -5

a = 14, b = -2

a - b = 12

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 8, b = 4

a = 20, b = 8

a = 0, b = 12

a = 15½, b = 3¼

b - a = 12

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 15, b = 3

a = 3, b = 15

a = 12, b = 12

a = 3½, b = 15½

a + b = 0

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 4, b = -4

a = -4, b = 4

a = 7, b = -7

a = 10, b = -10

a - b = 0

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 8, b = -8

a = 3, b = 3

a = -17, b = 17

a = 10¾, b = 10¾

b - a = 15

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 8, b = 7

a = 5, b = 10

a = -5, b = 10

a = ½, b = 15½

a - b = -5

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 8, b = 3

a = 3, b = 8

a = 15, b = 10

a = 5½, b = 10½

• Question 1

a + b = 7

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 4, b = 3
a = 3, b = 4
a = 10, b = -3
EDDIE SAYS
4 + 3 = 7
3 + 4 = 7
7 + 7 = 14
10 + -3 = 7
• Question 2

a - b = 5

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 8, b = 3
a = 17, b = 12
a = 10½, b = 5½
EDDIE SAYS
8 - 3 = 5
3 - 8 = -5
17 - 12 = 5
10½ - 5½ = 5
• Question 3

b - a = 5

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 3, b = 8
a = ½, b = 5½
EDDIE SAYS
3 - 8 = -5
8 - 3 = 5
12 - 17 = -5
5½ - ½ = 5
• Question 4

a + b = 12

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 8, b = 4
a = 14, b = -2
EDDIE SAYS
4 + 7 = 11
8 + 4 = 12
7 + -5 = 2
14 + -2 = 12
• Question 5

a - b = 12

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 20, b = 8
EDDIE SAYS
8 - 4 = 4
20 - 8 = 12
0 - 12 = -12
15½ - 3¼ = 12¼
• Question 6

b - a = 12

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 3, b = 15
a = 3½, b = 15½
EDDIE SAYS
3 - 15 = -12
15 - 3 = 12
12 - 12 = 0
15½ - 3½ = 12
• Question 7

a + b = 0

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 4, b = -4
a = -4, b = 4
a = 7, b = -7
a = 10, b = -10
EDDIE SAYS
4 + -4 = 0
-4 + 4 = 0
7 + -7 = 0
10 + -10 = 0
• Question 8

a - b = 0

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 3, b = 3
a = 10¾, b = 10¾
EDDIE SAYS
8 - -8 = 16
3 - 3 = 0
-17 - 17 = -34
10¾ - 10¾ = 0
• Question 9

b - a = 15

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = -5, b = 10
a = ½, b = 15½
EDDIE SAYS
7 - 8 = -1
10 - 5 = 5
10 - -5 = 15
15½ - ½ = 15
• Question 10

a - b = -5

Which of these solutions satisfy the equation?

Tick all the solutions that fit.

a = 3, b = 8
a = 5½, b = 10½
EDDIE SAYS
8 - 3 = 5
3 - 8 = -5
15 - 10 = 5
5½ - 10½ = -5
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