Q:

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:y &gt; β2x + 3y is less than 1 over 2 times x minus 2Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)Part B: Is the point (β2, 3) included in the solution area for the system? Justify your answer mathematically. (4 points)

Accepted Solution

A:
Answer:Part A) The description of the solution area in the procedurePart B) The ordered pair (β2, 3) is not included in the solution area for the systemStep-by-step explanation:Part A) we havey > -2x+3 -----> inequality AThe solution of the inequality A is the shaded area above the dashed line y=-2x+3The slope of the dashed line is negative (m=-2)The y-intercept of the dashed line is (0,3)The x-intercept of the dashed line is (1.5,0)y < (1/2)x-2 -----> inequality BThe solution of the inequality B is the shaded area beow the dashed line y=(1/2)x-2The slope of the dashed line is positive (m=1/2)The y-intercept of the dashed line is (0,-2)The x-intercept of the dashed line is (4,0)using a graphing toolThe solution of the system of inequalities is the shaded area between the two dashed linessee the attached figurePart B) Is the point (β2, 3) included in the solution area for the system? we know thatIf a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities of the systemVerify inequality ASubstitute the value of x=-2 and y=3 in the inequality A3 > -2(-2)+33 > 7 -----> is not truethereforeThe ordered pair (β2, 3) is not included in the solution area for the system