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Geometry - properties of shapes

Geometry - position and direction

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# Solving equations with two unknowns 0%

Summary

# 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 $\underline{1\times20p}$

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