Year 10 - Maths
Solving a quadratic and linear pair of simultaneous equations graphically
Simultaneous equations: 2 variables
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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 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 relate the solutions (0, 1 or 2) of a linear and quadratic pair of simultaneous equations to the graphs of these equations.
Key Notes
- You can use your knowledge of graphical representations to draw the graphs on the same axes.
- If there exists two solutions, then the points of intersection are those solutions.
- If there exists one solution, then the point where the linear graph touches the quadratic graph is that solution.
- If there are no solutions then the graphs do not touch at all.
- When substituting or eliminating, you are left with a combined quadratic which has roots where the graphs intersect.
Vocabulary To Learn
- Linear: The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.
- Quadratic: A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2; the graph of which forms a parabola.
Common Mistakes To Avoid
- For a pair of simultaneous equations (one linear and one quadratic), there will always be two intersections and therefore two solutions.
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 graphical representations to draw the graphs on the same axes. If there exists two solutions, then the points of intersection are those solutions.
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: For a pair of simultaneous equations (one linear and one quadratic), there will always be two intersections and therefore two solutions. Correction: The linear graph might be tangent to the curve therefore only one intersection (solution). Alternatively, the straight line may never intersect the parabola and in this case, there is no solution.
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 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
- Solving simultaneous linear equations graphically Study Guide
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