Which ordered pairs are in the solution set of the system of linear inequalities?

The correct answer is the first option: (5, -2) (3, 1) (-4, 2)

Step-by-step explanation:

Given the following systems of linear inequalities:

y ≥ -1/2x and y < 1/2x + 1:

Plugging in the values of (5, -2) (3, 1) (-4, 2) into the given systems of linear inequalities provides a true statement:

y ≥ -1/2x:

(5, -2):  y ≥ -1/2x

          -2 ≥ -1/2(5)

          -2 ≥ -2.5  True statement.

(5, -2): y < 1/2x + 1

           -2 < 1/2(5) + 1

          -2 < 3.5  True statement.

(3, 1):  y ≥ -1/2x

         3 ≥ -1/2( 1 )

         3  ≥ -1/2 True statement.

(3, 1): y < 1/2x + 1

        1 < 1/2(3) + 1

        1 < 2.5  True statement.

(-4, 2): y ≥ -1/2x

          2 ≥ -1/2(-4)

         2  ≥ 2 True statement.

(-4, 2): y < 1/2x + 1

          2 < 1/2(-4) + 1

          2 < -1 True statement.

Therefore, (5, -2) (3, 1) (-4, 2) are the solutions to the systems of linear inequalities.