Substitution

Exam code: 4024

Written by: Ashika|Reviewed by: Caroline Carroll|Updated 2 July 2026

Substitution

Substitution means replacing a letter (variable) in a formula with a given number

Write down the formula
Replace (substitute) the letters in the formula with the given numbers
- If substituting in a negative number, it is important to put brackets around it
  - For example, (-3)
Simplify any numerical calculations
Calculate the final value
Sometimes the result is an equation which you can then solve

Worked example

(a) Given that $x = 2$ and $y = - 4$ , find the value of the expression:

(i) $2 x (x + 3 y)$

(ii) $y^{2} + y^{3}$

Answer:

(i)

Substitute the numbers given
Use brackets () around negative numbers

$\begin{array}{cl} 2 \times 2 \times (2 + 3 \times (- 4)) \end{array}$

Complete the calculation
Show every step of working, following the order of operations correctly

$\begin{array}{rcl} = & 2 \times 2 \times (2 - 12) \\ = & 2 \times 2 \times (- 10) \\ = & 4 \times (- 10) \end{array}$

-40

(ii)

Substitute the numbers given
Use brackets () around negative numbers

${(- 4)}^{2} + {(- 4)}^{3}$

Work out the powers remembering to include the brackets

$16 + (- 64)$

Complete the calculation

$16 - 64$

-48

(b) The formula $P = 2 l + 2 w$ is used to find the perimeter, $P$ , of a rectangle of length $l$ and width $w$ .

Given that the rectangle has a perimeter of 20 cm and a width of 4 cm, find its length.

Answer:

Substitute the values you are given for $P$ and $w$ into the formula

$20 = 2 \times l + 2 \times 4$

Simplify

$20 = 2 l + 8$

Solve the resulting equation to find the value of $l$
Start by subtracting 8 from both sides

$12 = 2 l$

Divide both sides by 2

$l = 6 cm$

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