Linear Equations
A linear equation has an unknown to the power one and is solved by doing the same operation to both sides to isolate the unknown.
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A linear equation has an unknown to the power one and is solved by doing the same operation to both sides to isolate the unknown.
- Balance both sides at every step
- Undo operations in reverse order
- Check by substituting the answer
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Linear Equations?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Linear Equations. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Linear Equations in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Linear Equations gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Linear Equations in detail
A linear equation contains an unknown to the power one, such as 3x + 5 = 20. To solve it, do the same operation to both sides, keeping the equation balanced, until the unknown is on its own: subtract 5 to get 3x = 15, then divide by 3 to get x = 5.
If the unknown appears on both sides, collect the terms with x on one side first. Always check by substituting your answer into the original equation. Linear equations model everyday problems such as comparing phone plans, working out ages and finding unknown lengths.
How the interactive helps you understand Linear Equations
Move the slope and y-intercept sliders. The line and its equation update, so you can see how the slope sets the steepness and the intercept sets where the line crosses the y-axis.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Linear Equations.
Real-life uses and examples
- Spot Linear Equations in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Linear Equations by estimating first, then working it out step by step.
- Use Linear Equations when comparing prices, discounts or recipe quantities in everyday life.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Linear Equations.
- Memorising the steps for Linear Equations without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Linear Equations
What is Linear Equations?
A linear equation has an unknown to the power one and is solved by doing the same operation to both sides to isolate the unknown.
What are the most important points about Linear Equations?
The main points are: Balance both sides at every step; Undo operations in reverse order; Check by substituting the answer.
Why is Linear Equations useful?
Understanding Linear Equations gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Linear Equations?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Linear Equations?
Related topics in Mathematics include Simultaneous Equations, Completing the Square, Coordinates and Graphs.