Which system of linear inequalities is shown in the graph

The answer to your question is:

x + 2y - 4 ≥ 0     and     2x -y -3 > 0

Step-by-step explanation:

First look for two points of each line to fine the line equations

1 st line points:  (2, 1) ; (0, 2)

2nd line points: (2, 1) ; (3, 3)

1st line slope

                         m = (2 - 1) / (0 - 2) = 1 / -2  = -1/2

2nd line slope

                         m = (3 - 1) / ( 3 - 2) = 2 / 1 = 2

1st line

                    y - 1 = -1/2 (x - 2)

                    2y - 2 = -1(x - 2)

                    2y - 2 = -x + 2

                    x + 2y - 4 = 0        Inequality        x + 2y - 4 ≥ 0

2nd line

                 y - 1 = 2(x - 2)

                 y - 1 = 2x - 4

                 2x -y -3 = 0             Inequality          2x -y -3 > 0