determine the relationship between the point (1, -5) and the given system of inequalities. y ≤ 3x + 2 y >…

Explanation:

Step1: Substitute into first - inequality

Substitute (x = 1) and (y=-5) into (y\leq3x + 2). (-5\leq3\times1+2), since (3\times1 + 2=3 + 2=5) and (-5\leq5) is True.

Step2: Substitute into second - inequality

Substitute (x = 1) and (y = - 5) into (y>-2x-3). (-5>-2\times1-3), since (-2\times1-3=-2 - 3=-5) and (-5=-5), so (-5>-5) is False.

Step3: Determine the relationship

Since the point ((1,-5)) does not satisfy both inequalities simultaneously, the point ((1,-5)) is not a solution of the system of inequalities.

Graphically, the first inequality (y\leq3x + 2) represents the region below (and including) the line (y = 3x+2). The second inequality (y>-2x - 3) represents the region above the line (y=-2x - 3). When we graph these two lines and their respective regions, the point ((1,-5)) will be in the region of the first - inequality but not in the region of the second - inequality.

Answer:

The point ((1,-5)) is not a solution of the given system of inequalities.