which ordered pairs are in the solution set of the system of linear inequalities?\n$y\\geq…

Explanation:

Step1: Check (5, -2) in both inequalities

First inequality: $-2 \geq -\frac{1}{2}(5) \rightarrow -2 \geq -2.5$ (True).
Second inequality: $-2 < \frac{1}{2}(5) + 1 \rightarrow -2 < 3.5$ (True).

Step2: Check (3, 1) in both inequalities

First inequality: $1 \geq -\frac{1}{2}(3) \rightarrow 1 \geq -1.5$ (True).
Second inequality: $1 < \frac{1}{2}(3) + 1 \rightarrow 1 < 2.5$ (True).

Step3: Check (-4, 2) in both inequalities

First inequality: $2 \geq -\frac{1}{2}(-4) \rightarrow 2 \geq 2$ (True, equality holds).
Second inequality: $2 < \frac{1}{2}(-4) + 1 \rightarrow 2 < -1$ (False).

Step4: Check (3, -1) in both inequalities

First inequality: $-1 \geq -\frac{1}{2}(3) \rightarrow -1 \geq -1.5$ (True).
Second inequality: $-1 < \frac{1}{2}(3) + 1 \rightarrow -1 < 2.5$ (True).

Step5: Check (4, -3) in both inequalities

First inequality: $-3 \geq -\frac{1}{2}(4) \rightarrow -3 \geq -2$ (False).
Second inequality is irrelevant as first fails.

Step6: Check (4, 2) in both inequalities

First inequality: $2 \geq -\frac{1}{2}(4) \rightarrow 2 \geq -2$ (True).
Second inequality: $2 < \frac{1}{2}(4) + 1 \rightarrow 2 < 3$ (True).

Step7: Check (-3, 1) in both inequalities

First inequality: $1 \geq -\frac{1}{2}(-3) \rightarrow 1 \geq 1.5$ (False).
Second inequality is irrelevant as first fails.

Answer:

(5, -2), (3, 1), (4, 2)