The solution set is the region above both lines. Coordinates of a point in the solution set: (5, 0).
To solve the system of inequalities graphically, you need to plot the two lines corresponding to each inequality on the set of axes and identify the region where the shaded areas overlap.
Graph the first inequality:
y>−x−1
Start by plotting the y-intercept, which is (0,−1). Then, use the slope to find another point, for example, move one unit to the right and one unit up to get (1,−2).
Draw a dashed line through these points since the inequality is strict (>), indicating that the points on the line are not included in the solution.
Graph the second inequality:
y> 1/3x−5
Plot the y-intercept (0,−5) and use the slope to find another point, for example, move three units to the right and one unit up to get (3,−4).
Draw another dashed line through these points.
Identify the overlapping region:
The solution is the region where both shaded areas overlap. This is the region above both lines since both inequalities are >.
State coordinates of a point in the solution set:
Choose a point within the overlapping region. One such point is (5,0).
In conclusion, the solution set is the region above both lines, and a point in this set is (5,0).