Question

Solve the system of inequalities:

x + 2y < 5
x - y < 2
x > 0
y > 0

Answer 1

To solve the system of inequalities x + 2y < 5, x - y < 2, x > 0, and y > 0, graph each inequality and shade the corresponding regions. The solution is the overlapping shaded region.

Step-by-step explanation:

To solve the system of inequalities:

1. Start by graphing the first inequality, x + 2y < 5. Plot the boundary line x + 2y = 5 as a dotted line. Choose a test point that is not on the line, such as (0,0), and plug it into the inequality. If it satisfies the inequality, shade the region below the line. Otherwise, shade the region above the line.
2. Graph the second inequality, x - y < 2, in a similar manner. Plot the boundary line x - y = 2 as a dotted line. Use a test point, such as (0,0), to determine which side to shade.
3. Since the third inequality, x > 0, is already in the form of x > a, you can simply shade the region to the right of the y-axis.
4. The fourth inequality, y > 0, is already in the form of y > a. Shade the region above the x-axis.
5. The solution to the system of inequalities is the overlapping shaded region.