watch the video and then solve the problem given below.\nclick here to watch the video.\ngraph the solution…

watch the video and then solve the problem given below.\nclick here to watch the video.\ngraph the solution set of the following system of inequalities.\n$$ \\left\\{ \\begin{array} { l } { x - 2 y > 5 } \\\\ { 2 x + y \\leq - 5 } \\end{array} \\right. $$\nuse the graphing tool to graph the system.\nclick to\nenlarge\ngraph

watch the video and then solve the problem given below.\nclick here to watch the video.\ngraph the solution set of the following system of inequalities.\n$$ \\left\\{ \\begin{array} { l } { x - 2 y > 5 } \\\\ { 2 x + y \\leq - 5 } \\end{array} \\right. $$\nuse the graphing tool to graph the system.\nclick to\nenlarge\ngraph

Answer

Explanation:

Step1: Graph the line (2x + y=-5)

First, rewrite (2x + y=-5) as (y=-2x - 5). The slope (m=-2) and (y -)intercept (b =-5). Since the inequality is (2x + y\leq-5), we draw a solid line (because the inequality includes equality) and shade the region below the line.

Step2: Graph the line (x-2y = 5)

Rewrite (x-2y=5) as (y=\frac{1}{2}x-\frac{5}{2}). The slope (m = \frac{1}{2}) and (y-)intercept (b=-\frac{5}{2}). Since the inequality is (x - 2y>5), we draw a dashed line (because the inequality does not include equality) and shade the region below the line (test a point, say ((0,0)): (0-2\times0=0\not>5), so the region that does not contain ((0,0)) is shaded).

Step3: Find the intersection region

The solution set of the system of inequalities is the region that is shaded for both inequalities.

Answer:

The solution set is the intersection of the region below (or on) the line (y=-2x - 5) and the region below the line (y=\frac{1}{2}x-\frac{5}{2}) (excluding the line (x - 2y = 5)).