graph the solution set of the system: y>3x+2, y<2/3x+5, y>-2/5x-3 1/5, y>-1
To graph the solution set of the system of inequalities, follow these steps:
Step 1: Graph each inequality individually.
For the inequality y > 3x + 2:
Start by graphing the line y = 3x + 2. This can be done by plotting two points on the line and drawing a straight line through them. Since this inequality is a strict "greater than" inequality, you will need to use a dashed line to indicate that points on the line are not included in the solution.
For the inequality y < (2/3)x + 5:
Graph the line y = (2/3)x + 5 using the same process as in the previous step. Again, use a dashed line to indicate that points on the line are not included in the solution.
For the inequality y > (-2/5)x - 3 1/5:
Graph the line y = (-2/5)x - 3 1/5. This time, however, it is a "greater than or equal to" inequality, so use a solid line to indicate that points on the line are included in the solution.
For the inequality y > -1:
This is a horizontal line. Simply draw a horizontal line through y = -1.
Step 2: Identify the overlapping region.
The solution set of the system of inequalities is obtained by finding the region where all the shaded areas overlap. Areas that are shaded by more than one inequality satisfy more than one condition and are therefore included in the solution set.
Step 3: Shade the overlapping region.
Identify the overlapping region and shade it. This shaded region represents the solution set of the system of inequalities.
Remember to label the axes and any important points like intercepts or coordinates if any are present in the system.
Graphing the system in this way will help you visualize the solution set and see where the different inequalities overlap and satisfy the conditions.