Question 378809
Wow.  Your work simply jumps right out of the monitor like a genie :D!
In your first system, {{{y < 9 - x^2}}} has boundary a dashed parabola with y-intercept 9 and x-intercepts 3 and -3. The inequality {{{y >= x+3}}} has boundary a solid line y = x + 3. (It has y-int 3 and x-int -3).  Now use test points to determine which regions to shade.