Quick what are the solutions of the system? {y=2x+6 y=x^2+5x+6

If you were to graph these 2 functions, you would see that they intersect at the following points.    (-3,0) and (0,6)  so these would be your solutions

You could also solve this algebraically using substitution:
2x + 6 = x² + 5x + 6  
0 = x² + 5x + 6 - 2x - 6
0 = x² + 3x
0 = x(x + 3)  which implies x = 0 and x = -3  you can now plug these values in for x in the linear function to find the corresponding y coordinates.  

Hope this helps