01Why this matters
Formulas become useful when you can put measurements into them accurately. The same skill works for costs, geometry and physics.
02See it
03Understand it
Substitution means replacing a variable with a known value while preserving the operations around it.
Write the formula first, then replace each variable with its value. Use brackets around negative numbers and compound inputs. Keep units alongside values, and follow the order of operations. A formula may require specific units, so convert before substituting.
04Guided example
Evaluate y = 2x² + 3 when x = −2.
- Replace x with (−2): y = 2 × (−2)² + 3.
- Square the whole negative value: (−2) × (−2) = 4.
- Multiply and add: y = 2 × 4 + 3 = 11.
05Try it
06Practise it
07Use it in the real world
The distance formula d = vt gives d = 6 m/s × 5 s = 30 m for motion at constant speed. Seconds cancel, leaving metres.
Go a little deeper
Substitution can check a proposed solution: put it back into the original equation and compare both sides. This is often faster than solving the problem twice.
08Quick check
09Summary
Substitution means replacing a variable with a known value while preserving the operations around it. Multiply and add: y = 2 × 4 + 3 = 11.
Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.
10Key idea
y = 2x² + 3
x is the input and y is the output; this example uses dimensionless numbers.
Substitute with brackets: y = 2 × (input)² + 3
Find this in the formula library →