Find the coordinates of the two points where the lines y=x²+4x+6 and y=x+4 meet.

To solve these equations we must make them equal to eachother. This gives us x²+4x+6=x+4, we must then subtract the 'x+4' from both sides to give us an equation that equals 0. This gives us the following equation x²+3x+2=0. To solve this we can factorise it which gives us (x+1)(x+2)=0. To find the values of x we must make each bracket equal to 0 so we get x+1=0 -> x=-1 and x+2=0 -> x=-2. Now we have our values for x, we must find the y values, this can be done by substituting each x -value into our y equation (y=x+4). For x=-1, we get y=(-1)+4 -> y=3 so our coordinate is (-1,3), and for x=-2, we get y=(-2)+4 -> y=2 so our coordinate is (-2,2).