Year 10 - Maths
Solving simultaneous linear equations graphically
Simultaneous equations: 2 variables
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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 to solve a pair of simultaneous equations from different starting points and cases using a variety of strategies.
Lesson Summary
You will learn to solve two linear simultaneous equations graphically (0 or 1 or infinitely many solutions).
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
- 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
- Equations always have one solution.
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. 'Linear'
The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Equations always have one solution. Correction: Some equations have one solution but, some have no solutions, some have two solutions, some have more than two solutions.
More Lessons In This Unit
- Checking and securing understanding of interpreting graphs Study Guide
- Combining equations Study Guide
- Forming simultaneous equations Study Guide
- Problem solving with linear and quadratic simultaneous equations Study Guide
- Problem solving with simultaneous equations Study Guide
- Solving a quadratic and linear pair of simultaneous equations graphically Study Guide
- Solving a quadratic and linear pair of simultaneous equations using elimination Study Guide
- Solving a quadratic and linear pair of simultaneous equations using substitution Study Guide
- Solving algebraic simultaneous equations by elimination Study Guide
- Solving more complex simultaneous equations by elimination Study Guide
- Solving simultaneous equations by elimination from a context Study Guide
- Solving simultaneous equations via any method Study Guide
- Solving simultaneous linear equations by substitution Study Guide
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