-3x-7y<21 and -7x-9y<63
I need to label the intersection on the graph where these two points meet
First off, there are no "these two points."
Second, the solution to the system of inequalities is a whole region of the plane, not just a point.
If we are dealing with equations, then the point where the lines meet is (-126/11, 21/11)
The shaded region in the plot below shows the solution set.
www.wolframalpha.com/input/?i=solve+-3x-7y<21+and+-7x-9y<63
When you post a problem, try to make it actually mean something. There is no way the original exercise could have been worded as you wrote it. If so, run far, run fast from that instructor!!!