Year 11 - Maths
Checking and securing understanding of simultaneous equations
Inequalities
Study Hub
Study Guides
This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils extend their understanding of inequalities and consider a range of contextual inequalities and ways to find and represent their solutions.
Lesson Summary
You will learn to recognise that the point of intersection of two linear graphs satisfies both relationships and hence represents the solution to both those equations.
Key Notes
- You can use your knowledge of linear graphs to draw the graphs of both equations on the same axes
- If there exists a solution, the point of intersection is that solution
- If the lines are parallel then there are no solutions
- If the lines lie on top of each other, there are infinitely many solutions
Vocabulary To Learn
- Simultaneous equations: Equations which represent different relationships between the same variables are called simultaneous equations.
- Linear: The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.
Common Mistakes To Avoid
- Pupils may mix-up the x and y coordinates.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
You can use your knowledge of linear graphs to draw the graphs of both equations on the same axes. If there exists a solution, the point of intersection is that solution.
2. Use this key word in a maths sentence and explain it clearly. 'Simultaneous equations'
Equations which represent different relationships between the same variables are called simultaneous equations. 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 mix-up the x and y coordinates. Correction: Remind pupils that the x value is read from the x-axis and is read first. The y value is read from the y-axis and is read second.
More Lessons In This Unit
- A single solution set Study Guide
- Advanced problem solving with linear inequalities Study Guide
- Inequalities on number lines Study Guide
- Linear inequalities in context Study Guide
- Non-solutions to simultaneous linear equations Study Guide
- Problem solving with linear inequalities Study Guide
- Relating graphical solutions to algebraic solutions for inequalities Study Guide
- Solution set notation Study Guide
- Solving a linear inequality graphically Study Guide
- Solving a set of linear inequalities graphically Study Guide
- Solving more complicated linear inequalities Study Guide
- Solving quadratic inequalities algebraically Study Guide
- Solving quadratic inequalities in one variable graphically Study Guide
- Solving simple linear inequalities Study Guide
Browse all guides in the Year 11 Maths guide library.