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