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To find the turning points we need to find dy/dx and set it equal to zero. From there we can find the x coordinate and substitute it back into the origional equation to find the y coordinate.

To solve these equations, our aim is to find a value of x and a value of y that satisfy both equations at the same time. By satisfy we mean, if we plug our values in for x and y then the left hand side...

To solve these eliminations, we must eliminate either the x's or the y's. Either is possible but let us start with the y's. There is 2y in the first equation and (-1)y in the second, so we will have to...

This is a quadratic equation so there are two main methods you can use to solve it- factorising and completing the square.

My preferred method and the on...

While there are several ways to solve this, in this particular case I would favour the method of elimination. Since the value of y is the same and they have opposite signs, we can add the equations tog...