Year 8 - Maths
Many equations, one solution
Solving linear equations
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils will learn how to find a value that satisfies a linear relationship when one value is known both with a single step operation, and multiple step operations. A variety of cases are explored including using brackets and rearranging.
Lesson Summary
You will learn to understand that a family of linear equations can all have the same solution.
Key Notes
- Starting from a single value for a variable you can write equations that are equivalent.
- A solution to a linear equation is a value that makes the two sides equal .
- All the equivalent equations will have the same solution.
Vocabulary To Learn
- Solution: A solution to an equality with one variable is a value which, when substituted, maintains the equality between the expressions.
- Equation: An equation is used to show two expressions that are equal to each other.
Common Mistakes To Avoid
- Pupils may think a value has to be added to each term in an expression.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Starting from a single value for a variable you can write equations that are equivalent. A solution to a linear equation is a value that makes the two sides equal .
2. Use this key word in a maths sentence and explain it clearly. 'Solution'
A solution to an equality with one variable is a value which, when substituted, maintains the equality between the expressions. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may think a value has to be added to each term in an expression. Correction: When adding a term to an expression we can write it as a single addition and then collect like terms if necessary. Show with numbers first.
More Lessons In This Unit
- Brackets in equations Study Guide
- Checking understanding of algebraic notation Study Guide
- Different types of equations Study Guide
- Equality in an equation Study Guide
- Preparing to solve two step linear equations Study Guide
- Problem solving with linear equations Study Guide
- Rearranging to solve linear equations Study Guide
- Securing understanding of equality Study Guide
- Solution to an equation Study Guide
- Solving complex linear equations Study Guide
- Solving complex linear equations involving brackets Study Guide
- Solving linear equations graphically using technology Study Guide
- Solving linear equations where brackets are used Study Guide
- Solving simple linear equations with a multiplicative step Study Guide
- Solving simple linear equations with an additive step Study Guide
- Solving two step linear equations Study Guide
Browse all guides in the Year 8 Maths guide library.