# Substitution

## Substituting in variables

When substituting variables it is key to remember BIDMAS/ BODMAS and also what the relationship between the variables means. The letter stands for a variable and when we are given the value of that variable we can put it into a formula or equation to work out a specific value. (Like ‘subs’ in a sports match!)

Here’s how to substitute into a basic expression:

If a = 4 what is the value of 3a + 6?

Step 1: rewrite the equation with () in the place of letters.

= 3( ) + 6

Step 2: put the specified number in the bracket

=3(4) +6

Step 3: work out the equation

=3(4) +6

=12 +6

=18

## Substitution with more than one variable

You can use the same method we used for one variable when you have to substitute into harder equations with more than one variable and more calculations such as this: If t= 0.6 , r= -3 and w=½, what is:

=3t - 4r2**/** 4w + 2r

Step 1:

=3( ) - 4()2**/** 4( ) + 2( )

Step 2:

=3(0.6) - 4(-3)2__/ __4(½) + 2(-3)

This is important as this expression involves squaring decimals! Remember BIDMAS!

Step 3:

=1.8 - 36__/ __2 - 6

=-34.2**/** -4

=8.55

*Always check your answer!!*

- If e = 6 what is 3e +8?
- 26
- If d = -3 and r = 8 what is 5d + 4r - 6?
- 11
- If a = -5, b = -6, c = 4.5, What is a(squared) + 3b - 2c/ 6a -5
- Your answer should include: 2/3 / 2 3

Explanation:*⅔*