The cycle department of a toy store sells bicycles and tricycles.[br]George observes that there are 13 cycles in total. His brother James counts 31 wheels in total.[br][br]Is it possible to determine the number of bicycles and tricycles using only:[br][list=1][*]George's observation?[/*][*]James' observation?[/*][/list][br]What combination(s) of bicycles and tricycles satisfy:[br][list=1][*]George's observation?[/*][*]James' observation?[/*][*]both boys' observations?[/*][/list]

In the problem above, we can represent the observations of both boys using linear equations.[br]Suppose there are x bicycles and y tricycles.[br][br]Since there are 13 cycles in total, [math]x+y=13[/math].[br]Since there are 31 wheels in total, [math]2x+3y=31[/math].[br][br]We needs to find values for x and y which satisfy both equations at the same time.[br]We say that [math]\begin{matrix}x+y=13\\2x+3y=31\end{matrix}[/math] is a [b]system of simultaneous equations[/b].[br][br][br]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.[br][br]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.