Find the coordinates of the points where the lines y=x^2-5x+6 and y=x-4 intersect.

At the points of intersection the x and y coordinates will be the same. So we can solve the equations simultaneously to see what solutions to x and y solve both equations.Rearrange the second equation to get y=x+4, then set the two equations for y equal to each other.We get x^2-5x+6 = x+4.Rearrange this to get x^2-5x+6=0. So to factorise this we need two number which add to make -5, and multiply to make 6. Here -2 and -3 work, so we get (x-2)(x-3)=0.Solving this gives us x=2 or x=3.We can substitute these values into either of our original equations to obtain the corresponding y values. If x=2, y=x-4 = -2, or if x=3, y = x-4 = -1. So our solutions are (2, -2) and (3,-1). We can check these by substituting them into our other original equation to see if they are solutions... they are!