Year 8 - Maths
Solution to an equation
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 appreciate that a solution is a value that makes the two sides of an equation balance.
Key Notes
- In an expression the variable can take any value.
- In a linear equation there is a particular value that makes the equation balance.
- The value is the solution to the linear equation.
- When graphing a linear expression this value represents a single point.
Vocabulary To Learn
- Solution: A solution to an equality with one variable is a value which, when substituted, maintains the equality between the expressions.
Common Mistakes To Avoid
- When reading solutions from a graph pupils may read the solution as the y-coordinate.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
In an expression the variable can take any value. In a linear equation there is a particular value that makes the equation balance.
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: When reading solutions from a graph pupils may read the solution as the y-coordinate. Correction: The solution to the equation is the value of the variable that makes both sides balance.
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
- Many equations, one solution 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
- 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.