# Solve Equations with Two or More Variables

In this worksheet, students will be asked to solve equations with two or more variables.

Key stage:  KS 2

Curriculum topic:   Algebra

Curriculum subtopic:   Use Variables

Difficulty level:

### QUESTION 1 of 10

Remember, a letter simply represents a number in algebra.

Sometimes this may be set but sometimes it is up to you to work out what the number is worth.

Where a number can change is called a variable.

In this activity, all of the answers must be whole numbers or zero.

Example:

x + 3y = 8

What do we know?

What is set and what can't be changed?

What are we in control of? Why are these variables?

Through trial and error, we can find options:

The 3 different combinations can be shown in a bar model

 8
 x y y y 2 2 2 2 5 1 1 1 8 0 0 0

Can you choose two sets of variables that can represent

ab = 18?

a = 2 b = 9

a = 2 b = 6

a = 6 b = 3

a = 2 b =7

Can you choose two sets of variables that can represent

ab = 40?

a = 5 b = 6

a = 5 b = 8

a = 10 b = 4

a = 12 b =4

Can you find both possible variables for x and y in the equation below?

2x + y = 5?

 1 2 3 x y

Can you choose the two correct sets of variables for the equation below?

3x - 2y = 2?

x= 2 and y = 2

x = 10 and y = 12

x = 3 and y = 3

x = 4 and y = 5

Can you find three possible sets of variables for

2x + y = 7

a. x = 3 y = __

b. x =__  y = 5

c. x =__   y =__

 7
 x x y 3 3 5

x= 2 and y = 2

x = 10 and y = 12

x = 3 and y = 3

x = 4 and y = 5

Can you choose the 4 possible combinations of variables for the equation below?

6x + y = 29

x = 1 and y = 23

x = 7 and y = 2

x = 4 and y = 5

x = 8 and y = 9

x = 2 and y = 17

x = 3 and y = 11

I think of 2 numbers, when I triple one and multiply the other by 4 and then add both together, I get a total of 30

What can x and y be worth from the variables given?

3x + 4y = 30

 2 11 13 6 x y

I think of 2 numbers, when I multiply x by 3 and y by 2 and then subtract y from x, I get a total of 2.

Can you choose the correct value for x and y from the variables given?

3x - 2y = 2

 0 3 6 8 12 x y

How many possible variables are there for x and y for the equation below?

The variable cannot be greater than 10 and must be a whole number or 0.

2x - y = 7

2g + w = 15

g and w are positive, whole numbers.

Use a method of trial and error to complete the blank spaces below to find the variables for g and w.

• Question 1

Can you choose two sets of variables that can represent

ab = 18?

a = 2 b = 9
a = 6 b = 3
EDDIE SAYS
You should have noticed that there are more than two sets of variables for the expression ab = 18. The two correct options available were: 1. a = 2 and b = 9 as 2 x 9 = 18 2. a = 6 and b = 3 as 6 x 8 = 18 Another set of variables that would work for this equation are a = 1 and b = 18 as 1 x 18 = 18. Great focus, now let's get some real practise in!
• Question 2

Can you choose two sets of variables that can represent

ab = 40?

a = 5 b = 8
a = 10 b = 4
EDDIE SAYS
Again, as before, you may have realised that there are more than two sets of variables for the expression ab = 40. The two correct options available were: 1. a = 5 and b = 8 as 5 x 8 = 40 2. a = 10 and b = 4 as 10 x 4 = 40 Another set of variables that would work for this equation are a = 1 and b = 40 as 1 x 40 = 40 OR a =2 and b = 20 as 2 x 20 = 40. As you can see there is often more than one correct answer when solving equations!
• Question 3

Can you find both possible variables for x and y in the equation below?

2x + y = 5?

 1 2 3 x y
EDDIE SAYS
Did you select the correct options? Here are the possible combinations for 2x + y = 5: 1. x = 2 and y = 1 = (2 x 2) + 1 = 5 2. x = 1 and y = 3 = (2 x 1) + 3 = 5 Don't worry if you didn't get this one correct, but well done if you did!
• Question 4

Can you choose the two correct sets of variables for the equation below?

3x - 2y = 2?

x= 2 and y = 2
x = 4 and y = 5
EDDIE SAYS
Here we had two possible options for the equation 3x - 2y = 2: 1. x = 2 and y = 2 = (3x2) - (2x2) = 6 - 4 = 2 2. x = 4 and y = 5 = (3x4) - (2x5) = 12 - 10 = 2
• Question 5

Can you find three possible sets of variables for

2x + y = 7

a. x = 3 y = __

b. x =__  y = 5

c. x =__   y =__

 7
 x x y 3 3 5

EDDIE SAYS
A bar model helps us to use trial and error to work through the possible combination of variables we can use in an equation. Here are the answers we were looking for: a. x = 3 y = 1 so 2 x 3 = 6 + 1 = 7 b. x = 1 y = 5 so 2 x 1 = 2 + 5 = 7 c. x = 2 y = 3 so 2 x 2 = 4 + 3 = 7 Take a deep breath! You're halfway through the activity maths-whiz.
• Question 6

Can you choose the 4 possible combinations of variables for the equation below?

6x + y = 29

x = 1 and y = 23
x = 4 and y = 5
x = 2 and y = 17
x = 3 and y = 11
EDDIE SAYS
How did you do? The four correct combinations of variables were: 1. x = 1 and y = 23 so 6 x 1 = 6 + 23 = 29 2. x = 2 and y = 17 so 2 x 6 = 12 + 17 = 29 3. x = 3 and y = 11 so 3 x 6 = 18 + 11 = 29 4. x = 4 and y = 5 so 4 x 6 = 24 + 5 = 29
• Question 7

I think of 2 numbers, when I triple one and multiply the other by 4 and then add both together, I get a total of 30

What can x and y be worth from the variables given?

3x + 4y = 30

 2 11 13 6 x y
EDDIE SAYS
Did you get it? x =2 and y = 6, this is because: (3 x 2) = 6 + (4 x 6) = 24 6 + 24 = 30 The other variables resulted in answers greater than 30 therefore, couldn't be right.
• Question 8

I think of 2 numbers, when I multiply x by 3 and y by 2 and then subtract y from x, I get a total of 2.

Can you choose the correct value for x and y from the variables given?

3x - 2y = 2

 0 3 6 8 12 x y
EDDIE SAYS
How did you get on this time? So, x = 6 and y = 8, this works because: 3 x 6 = 18 and 2 x 8 = 16 18 - 16 = 2 The other variables given cannot result in the correct answer of 2. Hopefully, this is getting easier.
• Question 9

How many possible variables are there for x and y for the equation below?

The variable cannot be greater than 10 and must be a whole number or 0.

2x - y = 7

5
EDDIE SAYS
There are five possible combinations of variables for the equation: 2x - y = 7 1. x = 4 and y = 1 2. x = 5 and y = 3 3. x = 6 and y = 5 4. x = 7 and y = 7 5. x = 8 and y = 9
• Question 10

2g + w = 15

g and w are positive, whole numbers.

Use a method of trial and error to complete the blank spaces below to find the variables for g and w.

EDDIE SAYS
Did you complete the 4 possible solutions given? In total, there were 8 possible solutions for 2g+ w = 15. Here they are: 1. g=1 w=13 2. g=2 w=11 3. g=3 w=9 4. g=4 w=7 5. g=5 w=5 6. g=6 w=3 7. g=7 w=1 8. g=0 w= 15 Well done! That's another activity completed. Why not attempt another one in order to consolidate your knowledge?
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