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

2. Module C1
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3. The exact values can be found by solving the equations simultaneously
Suppose we want to find where 2 lines meet.
e.g 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

4. 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

5. 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

6. 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