Question

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y < 4x − 2 y is greater than or equal to negative 5 over 2 times x minus 2 Part 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 (−2, −2) included in the solution area for the system? Justify your answer mathematically. (4 points)

Answer 1

Part A:
 The first thing you should do is to graph both lines. Notice that one is of positive slope and another of negative slope.
 The solution of the inequation system is given by the shaded region. That is, all the points that are in the shaded region satisfy the system of inequations.
 Part B:
 the point (-2, -2) is NOT included in the solution area (it is not in the shaded region.
 Mathematically it is demonstrated by substituting inequalities and seeing that they are not satisfied
 inequality 1
 -2 <4 (-2) - 2
 -2 <-10 (false)
 inequality two
 -2> = - (5/2) (- 2) - 2
 -2> = 3 (false).