Question

state the coordinates of a point in the solution set.

\\y \ge x - 8\\
\\y < -\frac{3}{2}x - 3\\

Explanation:

Identify the system of inequalities

The given system is:

$$
LATEXBLOCK0
$$

Test a candidate point

Let's test the point \((0, -5)\):
For the first inequality:

$$ -5 \ge 0 - 8 \implies -5 \ge -8 \quad (\text{True}) $$

For the second inequality:

$$ -5 < -\frac{3}{2}(0) - 3 \implies -5 < -3 \quad (\text{True}) $$

Confirm the solution point

Since \((0, -5)\) satisfies both inequalities, it is in the solution set.

Answer:

\((0, -5)\)