Replace each letter with its value
If y = 2x + 1 and x = 4, then y = 2(4) + 1.
Write the value into the formula before simplifying.
Year 7
Substitute into formulae
Replace variables with values accurately, use brackets where needed, and evaluate formulae in algebraic and real-life contexts.
Lesson overview
Algebra - substitution and formulae
A formula shows a rule using letters. To substitute, replace each letter with its given value and then calculate carefully. It helps to write the value into the formula first, especially when the variable appears more than once. Brackets keep the structure clear and reduce sign errors.
Use brackets when a variable is repeated
If P = 2l + 2w, l = 5 and w = 3, then P = 2(5) + 2(3).
| Formula | Values | Substitution |
|---|---|---|
| P = 2l + 2w | l = 5, w = 3 | P = 2(5) + 2(3) |
Substitute every appearance of each variable.
Formulae can describe real contexts
If the total cost is C = 3n + 2 and n = 6, then the cost is 20.
The algebraic rule and the context say the same thing.
Worked example
Work out A = lw when l = 7 and w = 4.
| Formula | Substitute | Answer |
|---|---|---|
| A = lw | A = 7 x 4 | A = 28 |
- Write the formula A = lw.
- Replace l with 7 and w with 4.
- Calculate 7 x 4.
- So A = 28.
Try it
Substitute the values first, then work through the arithmetic carefully.
Question 1
If y = 3x + 2 and x = 4, what is y?
Question 2
If P = 2l + 2w, l = 5 and w = 3, what is P?
| l | w |
|---|---|
| 5 | 3 |
Question 3
If C = 4n + 1 and n = 6, what is C?
Question 4
If A = lw, l = 7 and w = 4, what is A?
Question 5
If s = 200 - 15t and t = 8, what is s?
Common mistakes
Watch for these when working through the lesson.
- Replacing only one occurrence of a variable when it appears more than once.
- Forgetting to multiply after substitution, such as writing 2(5) as 25.
- Mixing up which value belongs to which letter.
Related topics
These ideas fit closely with this lesson.
- Simplify linear expressions.
- Generate and explain sequences.
- Prime factorisation and factor pairs.