Final answer:
To graph the solution of the system of linear inequalities x-y>=2 and x+y<=9, plot the lines representing each inequality and shade the region where they intersect.
Step-by-step explanation:
To graph the solution of the system of linear inequalities x-y>=2 and x+y<=9, we first need to graph the lines representing each inequality.
For the inequality x-y>=2, let's rearrange it to y<=x-2. We can plot this line by finding two points that lie on it. For example, when x=0, y= -2, and when x=4, y=2. Connecting these points will give us a solid line.
For the inequality x+y<=9, let's rearrange it to y<=-x+9. Again, we can find two points on the line, such as when x=0, y=9, and when x=7, y=2. Connecting these points will give us a solid line.
The shaded region where both lines intersect represents the solution to the system of inequalities.