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8: Simultaneous Equations and Intersections © Christine Crisp Teach A Level Maths Vol. 1: AS Core Modules

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Simultaneous Equations and Intersections Module C1 "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

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Simultaneous Equations and Intersections Suppose we want to find where 2 lines meet. The point of intersection has an x -value between -1 and 0 and a y -value between 3 and 4. e.g. 1 and Sketching the lines gives The exact values can be found by solving the equations simultaneously

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Simultaneous Equations and Intersections As the y -values are the same, the right-hand sides of the equations must also be the same. At the point of intersection, we notice that the x -values on both lines are the same and the y - values are also the same. Substituting into one of the original equations, we can find y : The point of intersection is

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Simultaneous Equations and Intersections Sometimes the equations first need to be rearranged: Substituting into (1): The point of intersection is Solution: Equation (2) can be written as Now, eliminating y between (1) and (2a) gives: e.g. 2

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Simultaneous Equations and Intersections Exercises Point of intersection is Eliminate y : Rearrange (1): Eliminate y : Find the point of intersection of the following pairs of lines: Solution:

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