Solving a quadratic and linear pair of simultaneous equations graphically
I can relate the solutions (0, 1 or 2) of a linear and quadratic pair of simultaneous equations to the graphs of these equations.
Solving a quadratic and linear pair of simultaneous equations graphically
I can relate the solutions (0, 1 or 2) of a linear and quadratic pair of simultaneous equations to the graphs of these equations.
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Lesson details
Key learning points
- 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.
Keywords
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 misconception
For a pair of simultaneous equations (one linear and one quadratic), there will always be two intersections and therefore two solutions.
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.
To help you plan your year 10 maths lesson on: Solving a quadratic and linear pair of simultaneous equations graphically, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Solving a quadratic and linear pair of simultaneous equations graphically, download all teaching resources for free and adapt to suit your pupils' needs.
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Starter quiz
6 Questions
Exit quiz
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