Opening problem
Bicycles and tricycles
The cycle department of a toy store sells bicycles and tricycles.
George observes that there are 13 cycles in total. His brother James counts 31 wheels in total.
Is it possible to determine the number of bicycles and tricycles using only:
- George's observation?
- James' observation?
- George's observation?
- James' observation?
- both boys' observations?
Simultaneous equations
In the problem above, we can represent the observations of both boys using linear equations.
Suppose there are x bicycles and y tricycles.
Since there are 13 cycles in total, .
Since there are 31 wheels in total, .
We needs to find values for x and y which satisfy both equations at the same time.
We say that is a system of simultaneous equations.
In the previous chapter, we said that the graphed line was formed by the points (x,y) whose coordinates were solutions of the equation. Ignoring the fact that in the problem x and y are natural numbers, graph both equations and find the point of intersection between them. This point is the common solution between both equations.
If you can't see the lines or the intersection between them, you can drag the graphing space with your mouse until it's visible.