How do I solve an equation with two unknowns?

The easiest way to test out all the solutions is by using a table. Use trial and error to test every possible solution until you have found them all.

Unlimited power

Get the whole package!

Learn without limits

Explainer videos without evulpo advertising

Unlimited number of exercises

Printable summaries

Learn without limits

Weekly learning report

Cancel any time

From £ 6.67 /month

Benefit from a yearly subscription now!

Save 44%

~~£11.99 / Month~~

Save 44%

£6.67 / Month

Chapter overview

Learning goals

Maths

Solving equations with two unknowns

Your lesson progress

Summary

Download

Solving equations with two unknowns

In a nutshell

An equation with two unknowns is an equation with two variables that you do not know the value of. In some cases there may only be one solution, in others there may be a few and in many cases there could be infinite solutions!

Finding solutions to equations with two unknowns

Finding the solutions is all about using trial and error - trying out every possible solution.

Example 1

What are the possible whole number solutions to $2x + 4y = 16$ ?

$x$	$y$	$2x+4y$
$0$	$4$	$0+16=16$
$2$	$3$	$4+12=16$
$4$	$2$	$8+8=16$
$6$	$1$	$12+4=16$
$8$	$0$	$16+0 = 16$

There are five pairs of solutions: $\underline{(0,4) , (2,3) , (4,2) , (6,1)}$ and $\underline{(8,0)}$ .

Using a table

The easiest way to test out all the solutions is by using a table.

Example 2

Alex has some $20p$ and $50p$ coins. He has $£2.70$ all together. How many of each coin could he have?

Using a table:

$50p$	$20p$	$50x+20y=?$
$1$	$11$	$£2.70$
$2$	not possible
$3$	$6$	$£2.70$
$4$	not possible
$5$	$1$	$£2.70$

There are three possible combinations of coin that Alex could have:

$\underline{1\times50p}$ and $\underline{11 \times 20p}$

$\underline{3\times50p}$ and $\underline{6\times20p}$ 

$\underline{5\times50p}$ and $\underline{1\times20p}$ 

Solving equations with two unknowns

In a nutshell

Finding solutions to equations with two unknowns

Finding the solutions is all about using trial and error - trying out every possible solution.

Example 1

What are the possible whole number solutions to $2x + 4y = 16$ ?

$x$	$y$	$2x+4y$
$0$	$4$	$0+16=16$
$2$	$3$	$4+12=16$
$4$	$2$	$8+8=16$
$6$	$1$	$12+4=16$
$8$	$0$	$16+0 = 16$

There are five pairs of solutions: $\underline{(0,4) , (2,3) , (4,2) , (6,1)}$ and $\underline{(8,0)}$ .

Using a table

The easiest way to test out all the solutions is by using a table.

Example 2

Alex has some $20p$ and $50p$ coins. He has $£2.70$ all together. How many of each coin could he have?

Using a table:

$50p$	$20p$	$50x+20y=?$
$1$	$11$	$£2.70$
$2$	not possible
$3$	$6$	$£2.70$
$4$	not possible
$5$	$1$	$£2.70$

There are three possible combinations of coin that Alex could have:

$\underline{1\times50p}$ and $\underline{11 \times 20p}$

$\underline{3\times50p}$ and $\underline{6\times20p}$ 

$\underline{5\times50p}$ and $\underline{1\times20p}$ 

Frequently Asked Questions (FAQ)

FAQs

Question: How do I solve an equation with two unknowns?

Answer: The easiest way to test out all the solutions is by using a table. Use trial and error to test every possible solution until you have found them all.
Question: Can an equation with two unknowns have more than one solution?

Answer: In some cases there may only be one solution, in others there may be a few and in many cases there could be infinite solutions!
Question: What is an equation with two unknowns?

Answer: An equation with two unknowns is an equation with two variables that you do not know the value of.

Theory

Exercises

Your data protection

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners who may combine it with other information that you’ve provided them or that they’ve collected from your use of their services. By clicking on either "Accept cookies" or "Necessary cookies only", you agree to this (read more in our Privacy Policy). Privacy Policy

Unlimited power

Learn without limits

Benefit from a yearly subscription now!

Solving equations with two unknowns

Solving equations with two unknowns

​​In a nutshell

Finding solutions to equations with two unknowns

Example 1

Using a table

Example 2

Solving equations with two unknowns

​​In a nutshell

Finding solutions to equations with two unknowns

Example 1

Using a table

Example 2

Now you’ve read the summary, have a go at the exercises!

In a nutshell

In a nutshell