Edexcel IGCSE Maths 复习笔记 2.15.1 Quadratic Simultaneous Equations
Edexcel IGCSE Maths 复习笔记 2.15.1 Quadratic Simultaneous Equations
What are quadratic simultaneous equations?
- When there are two unknowns (say x and y) in a problem, we need two equations to be able to find them both: these are called?Simultaneous Equations
- If there is an x2?or y2?in one of the equations then they are?Quadratic?(or?Non-Linear) Simultaneous Equations
(They can be represented by a straight line and a curve on a graph – the two pairs of answers are the points of intersection of the line and the curve)
How do you solve quadratic simultaneous equations?
- This is called the?Substitution Method:Label?the equations?A?and?B
- Rearrange the?linear?equation to?y = …?(or?x = …)
- Substitute?for?y?(or?x) in the?quadratic?equation
- Multiply out?brackets
- Rearrange?to “quadratic = 0”
- Solve?using appropriate method (Factorisation or Formula)
- Substitute?back into the linear equation to find the other variable
- Check?your answer by substituting into the equation you didn’t use in 6
Exam Tip
If the resulting quadratic has a?repeated root?then the line is a?tangent?to the curve.If the resulting quadratic has?no roots then the line does not intersect with the curve – or you have made a mistake!When giving your final answer, make sure you indicate which x and y values go together. If you don’t make this clear you can lose marks for an otherwise correct answer.
Worked Example
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