Question

How do you graph the solution set of a system of inequalities? x-y≤3 x+y≤3

Answer 1

To graph the solution set of a system of inequalities, plot each inequality on the same coordinate plane and shade the appropriate region. The solution set is the region where the shaded regions overlap.

Step-by-step explanation:

To graph the solution set of a system of inequalities, we start by graphing each inequality on the same coordinate plane. In this case, we have two inequalities: x-y ≤ 3 and x+y ≤ 3. We can start by graphing x-y ≤ 3:

1. Plot the line x-y = 3. This line passes through the points (0, -3) and (3, 0), among others.
2. Since we want to represent x-y ≤ 3, we need to shade the region below the line.

Next, we graph x+y ≤ 3:

1. Plot the line x+y = 3. This line passes through the points (0, 3) and (3, 0), among others.
2. Since we want to represent x+y ≤ 3, we need to shade the region below the line.

The solution set of the system of inequalities is the region where the shaded regions of both inequalities overlap. This region represents the values of x and y that satisfy both inequalities.