On a graph, the lines with the equations y=x^2+5x+4 and y=-3x-8 meet at two distinct points. Find the coordinates of these meeting points.

y=x^2+5x+4 y=-3x-8 Equate the two equations: x^2+5x+4 = -3x-8Rearrange so that all values are on one side: x^2+8x+12=0 Factorise the equation by finding two values that multiply to give 12 and add together to give 8: (x+6)(x+2)=0 The x coordinate for the meeting points will be given by the values of x that make each respective set of brackets equal to zero: Therefore x= -6 and x= -2 To find the y coordinate substitute your x values back into one of the equations: y= -3(-6) -8 =10 y= -3(-2) -8 = -2 Therefore the coordinates are (-6,10) and (-2,-2)