# Understand How to Solve Equations with Two Unknowns

In this worksheet, students will be asked to solve a range of harder equations with two unknowns.

Key stage:  KS 2

Curriculum topic:   Algebra

Curriculum subtopic:   Use Equations

Difficulty level:

### QUESTION 1 of 10

This worksheet includes different questions that have equations with two unknowns.

The two letters in each equation stand for two numbers. Note: these numbers could be different or the same.

Example:

3x - 2y = 2

Which of the solutions satisfy the equation?

x= 6    y = 2

x =8    y = 4

x =4    y = 5

x = 10    y = 2

As you have been given options, put each pair into the equation to see if it can give the equation 3x - 2y = 2.

Remember to carry out any calculation in brackets first.

x= 2    y = 2

fits because (3 x 2) - (2 x 2) = 6 - 4 = 2

x =8    y = 4

does not fit because (3 x 8) - (2 x 4) = 24 - 8 = 16

x =4    y = 5

fits because (3 x 4) - (2 x 5) = 12 - 10 = 2

x = 10    y = 2

does not fit because

(3 x 10) - (2 x 2) = 30 - 4 = 26

Remember to use a sensible process of trial and error when solving equations with two unknowns.

x - 2y = 11

Which of these solutions satisfy the equation?

x=20, y=7

x=15, y=2

x=20, y=4.5

x=30, y=12

4x - 2y = 10

Which of these solutions satisfy the equation?

x=6, y=3

x=4, y=5

x = 20, y=35

x=10, y=15

For the following equation, can you match each solution to either 'correct' or 'incorrect'?

3x - y = 13

## Column B

x = 6, y = 5
Correct
x = 10, y = 17
Incorrect
x = 3, y = 2
Incorrect
x = 5, y = 1
Correct

For the following equation, can you match each solution to either 'correct' or 'incorrect'?

10p - 3q = 1

## Column B

p = 7, q = 6
Incorrect
p = 10, q = 3
Incorrect
p= 1, q = 3
Incorrect
p = 2, q = 6
Correct

For the following equation, can you match each solution to either 'correct' or 'incorrect'?

5c - 4d = 4

## Column B

c = 10, d = 4
Correct
c = 4, d = 4
Incorrect
c = 10, d = 9
Incorrect
c = 10, d = 11.4
Correct

For the following equation, can you complete the blank space to find the solution?

4m - 3n = 8

## Column B

c = 10, d = 4
Correct
c = 4, d = 4
Incorrect
c = 10, d = 9
Incorrect
c = 10, d = 11.4
Correct

For the following equation, can you complete the blank space to find the solution?

5s + 3t = 34

## Column B

c = 10, d = 4
Correct
c = 4, d = 4
Incorrect
c = 10, d = 9
Incorrect
c = 10, d = 11.4
Correct

For the following equation, if y = 5, what must x be worth?

6x + y = 29

For the following equation, if f = 7, what must e be worth?

9e + 4f = 100

For the following equation, if t = 6, what must u be worth?

8t - 3u = 15

• Question 1

x - 2y = 11

Which of these solutions satisfy the equation?

x=15, y=2
x=20, y=4.5
EDDIE SAYS
Here are the solutions, given from the pairs of numbers. 20 - (2 x 7) = 20 - 14 = 6 15 - (2 x 2) = 15 - 4 = 11 20 - (2 x 4.5) = 20 -9 = 11 30 - (12 x 2) = 30 - 24 = 6
• Question 2

4x - 2y = 10

Which of these solutions satisfy the equation?

x = 20, y=35
x=10, y=15
EDDIE SAYS
Here are the solutions given, from the pairs of numbers. (4 x 6) - (2 x 3) = 24 - 6 = 18 (4 x 4) - (2 x 5) = 16 - 10 = 6 (4 x 20) - (2 x 35) = 80 - 70 = 10 (4 x 10) - (2 x 15) = 40 - 30 = 10
• Question 3

For the following equation, can you match each solution to either 'correct' or 'incorrect'?

3x - y = 13

## Column B

x = 6, y = 5
Correct
x = 10, y = 17
Correct
x = 3, y = 2
Incorrect
x = 5, y = 1
Incorrect
EDDIE SAYS
Work through each option carefully to find the correct solutions. (3 x 6) - 5 = 18 - 5 = 13 (3 x 10) - 17 = 30 - 17 = 13 (3 x 3) - 2 = 9 - 2 = 7 (3 x 5) - 1 = 15 - 1 = 14
• Question 4

For the following equation, can you match each solution to either 'correct' or 'incorrect'?

10p - 3q = 1

## Column B

p = 7, q = 6
Incorrect
p = 10, q = 3
Incorrect
p= 1, q = 3
Correct
p = 2, q = 6
Incorrect
EDDIE SAYS
Work through each option carefully to find the correct solution, this time there was only one. (10 x 7) - (3 x 6) = 70 - 18 = 52 (10 x 10) - (3 x 3) = 100 - 9 = 91 (10 x 1) - (3 x 3) = 10 - 9 = 1 (10 x 2) - (3 x 6) = 20 - 18 = 2
• Question 5

For the following equation, can you match each solution to either 'correct' or 'incorrect'?

5c - 4d = 4

## Column B

c = 10, d = 4
Incorrect
c = 4, d = 4
Correct
c = 10, d = 9
Incorrect
c = 10, d = 11.4
Correct
EDDIE SAYS
Work through each option carefully to find the correct solution, this time we had two to find. (5 x 10) - (4 x 4) = 50 - 16 = 34 (5 x 4) - (4 x 4) = 20 - 16 = 4 (5 x 10) - (4 x 9) = 50 - 36 = 14 (5 x 10) - (4 x 11.5) = 50 - 46 = 4
• Question 6

For the following equation, can you complete the blank space to find the solution?

4m - 3n = 8

EDDIE SAYS
m= 5 This allows us to satisfy the equation: (4 x 5) - (3 x 4) = 8 20 - 12 = 8 Great focus.
• Question 7

For the following equation, can you complete the blank space to find the solution?

5s + 3t = 34

EDDIE SAYS
t = 3 This allows us to satisfy the equation: (5 x 5) + (3 x 3) = 34 25 + 9 = 34
• Question 8

For the following equation, if y = 5, what must x be worth?

6x + y = 29

4
EDDIE SAYS
6x + y = 29 (6 x 4) + 5 = 29 24 + 5 = 29 x = 4 and y = 5
• Question 9

For the following equation, if f = 7, what must e be worth?

9e + 4f = 100

8
EDDIE SAYS
9e + 4f = 100 (9 x 8) + (4 x 7) = 100 72 + 28 = 100 e = 8 and f = 7
• Question 10

For the following equation, if t = 6, what must u be worth?

8t - 3u = 15

11
EDDIE SAYS
8t - 3u = 15 (8 x 8) + (3 x 11) = 15 48 - 33 = 15 e = 8 and f = 7
---- OR ----

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