MATH SOLVE

7 months ago

Q:
# Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:y > β2x + 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 (β2, 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 (β2, 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 (β2, 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 (β2, 3) is not included in the solution area for the system