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

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" 2

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

Substituting into one of the original equations, we can find y: 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. As the y-values are the same, the right-hand sides of the equations must also be the same. Substituting into one of the original equations, we can find y: The point of intersection is

Sometimes the equations first need to be rearranged: e.g. 2 Solution: Equation (2) can be written as Now, eliminating y between (1) and (2a) gives: Substituting into (1): The point of intersection is 5

Exercises Find the point of intersection of the following pairs of lines: 1. Solution: Eliminate y: Point of intersection is 2. Rearrange (1): Solution: Eliminate y: Point of intersection is