Year 11 - Maths
Non-solutions to simultaneous linear equations
Inequalities
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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 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 identify what happens to the equations when a point other than the intersection is substituted into the equations.
Key Notes
- If a point on neither line is substituted into the equations, neither equation will be valid
- If a point on one of the lines is substituted into the equations, one equation will be valid
- Depending on the location of the point, the equation may evaluate to a bigger or smaller value
- Replacing the equals sign with an inequality sign would make the statement true
Vocabulary To Learn
- Simultaneous equations: Equations which represent different relationships between the same variables are called simultaneous equations.
- Inequality: An inequality is used to show that one expression may not be equal to another.
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.
If a point on neither line is substituted into the equations, neither equation will be valid. If a point on one of the lines is substituted into the equations, one equation will be valid.
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
- Checking and securing understanding of simultaneous equations Study Guide
- Inequalities on number lines Study Guide
- Linear inequalities in context 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.