Graph each inequality. The solution will be the intersection, or overlap, of the shaded regions.
Practice makes perfect
Graphing a single inequality involves two main steps.
Plotting the boundary line.
Shading half of the plane to show the solution set.
For this exercise, we need to do this process for each of the inequalities in the system.
x<3 & (I) y≥- 4 & (II)
The system's solution set will be the intersection of the shaded regions in the graphs of (I) and (II). We will graph the inequalities one at a time and then combine the graphs.
Inequality I
The inequality x<3 describes all values of x that are less than 3. This means that the boundary line will be vertical and we will shade the plane on the left-hand side. Notice that the inequality is strict, so the boundary line will be dashed.
Inequality II
The inequality y≥- 4 describes all values of y that are greater than or equal to - 4. This means that the boundary line will be horizontal and we will shade the plane above it. Notice that the inequality is notstrict, so the boundary line will be solid.
Combining the Inequality Graphs
Let's draw the graphs of the inequalities on the same coordinate plane.
The solution to the given system is the overlapping region, or the intersection of the shaded regions.
