**Substitution with Multiple Variables** *KS3 Revision*

## What you need to know

**Things to remember:**

- Substitution just means replacing a letter with a number.
- We don’t write \times when there is a number before a letter, so you need to remember that it is hiding there!
- xy=x\times y

- A fraction is another way of writing a division question.

We have looked at substituting for a single variable before, so let’s have a quick look back at how we did that first.

* *

*Use substitution to find the value of 5x when x = 13*

5x=5\times x=5\times13=65

Divisions questions could either appear as a division:

*Use substitution to find the value of x\div3 when x = 9*

* *

x\div3=9\div3=3

* *

Or as a fraction that we have to change:

*Use substitution to find the value of \frac{20}{x} when x = 5*

\frac{20}{x}=20\div x=20\div5=4

When we are substituting for two variables we do it in the exact same way, we just have to substitute for two variables!

*Use substitution to find the value of x+y when x = 13 and y = 11*

* *

x+y=13+11=24

* *

*Use substitution to find the value of x-y when x = 4 and y = 9*

* *

x-y=4-9=-5

* *

*Use substitution to find the value of xy when x = 13 and y = 12*

* *

xy=x\times y=13\times 12= 156

* *

*Use substitution to find the value of x\div y when x = 72 and y = 9*

* *

x\div y= 72\div9=8

* *

*Use substitution to find the value of \frac{x}{y} when x =64 and y = 8*

* *

*Hint:** Remember, a fraction is just another way of writing a division.*

* *

\frac{x}{y}=x\div y= 64\div8=8

## Example Questions

**Question 1:** *Use substitution to find the value of xy when x = 7 and y = 11*

xy=x\times y=7\times 11= 77

**Question 2:** *Use substitution to find the value of \frac{y}{x} when x = 7 and y = 35*

\frac{y}{x}=y\div x= 35\div7=5