Simultaneous equations: an insight from playing with technology
I've noticed a couple of tweets recently about the importance of being playful when doing mathematics and this has brought to mind an insight I had about simultaneous linear equations that occurred when I was being playful with them in technology. As a result of this I now have a different method for solving that I prefer to the standard textbook approaches. Playing with simultaneous equations In trying to construct a pair of linear simultaneous equations where the solution went through a given point. I can't remember the point but I'll use (3,2) for the example. I did this by creating a point A at (3,2) then two more points B and C and finding the lines that went through these and A. This gave me the simultaneous equations: 3 x + y = 11 x + 5 y = 13 I then moved the points B and C around to find some different equations that would have the same point of intersection. This is probably best displayed here by showing all the different lines I got in a...