Simultaneous equations

For me this is where equations get interesting, when you have to work out the right answer from two equations at the same time. The mathematical expression for this is 'simultaneous equations'. You are given two equations, say y=x and y=2x. If you think of these two equations as lines on a graph then you are being asked where the two lines cross. The first equation is a diagonal line going up from left to right. y=2x does exactly the same but this line is twice as steep. The number 2 is the steepness of the line and in mathematics it is called the gradient.

It is a lot simpler to know where these two lines cross by working out the simultaneous equations. You have y=x and y=2x. Where these two lines cross the xs are the same and the ys are the same. This means that you know that x =2x. How can this be? The only number possible for x is zero. If you draw the graphs you will see that zero is the only possible answer.

That sums it up