33. Open-Ended Write and graph a system of inequalities for which the solution is bounded by a dashed vertical line and a solid horizontal line.
34. Writing Explain how you determine where to shade when solving a system of inequalities.
35. Given a system of two linear inequalities, explain how you can pick test points in the plane to determine where to shade the solution set.

In Exercises 36–45, identify the inequalities A, B, and C for which the given ordered pair is a solution.

1. x + y ≤ 2 x plus y less than or equal to 2

   

2. y ≤ 3 2 x − 1 y less than or equal to , 3 halves , x minus 1

   

3. y > − 1 3 x − 2 y greater than negative , 1 third , x minus 2

   

36. (0, 0)
37. ( − 2 , − 5 ) open negative 2 comma negative 5 close
38. ( − 2 , 0 ) open negative 2 comma 0 close
39. ( 0 , − 2 ) open 0 comma negative 2 close
40. ( − 15 , 15 ) open negative 15 comma 15 close
41. (3, 2)
42. (2, 0)
43. ( − 6 , 0 ) open negative 6 comma 0 close
44. ( 4 , − 1 ) open 4 comma negative 1 close
45. ( − 8 , − 11 ) open negative 8 comma negative 11 close

Solve each system of inequalities by graphing.

46. { x + y < 8 x ≥ 0 y ≥ 0 left brace . table with 3 rows and 1 column , row1 column 1 , x plus y less than 8 , row2 column 1 , x greater than or equal to 0 , row3 column 1 , y greater than or equal to 0 , end table
47. { 2 y − 4 x ≤ 0 x ≥ 0 y ≥ 0 left brace . table with 3 rows and 1 column , row1 column 1 , 2 y minus 4 x less than or equal to 0 , row2 column 1 , x greater than or equal to 0 , row3 column 1 , y greater than or equal to 0 , end table
48. { y ≥ − 2 x + 4 x > − 3 y ≥ 1 left brace . table with 3 rows and 1 column , row1 column 1 , y greater than or equal to negative 2 x plus 4 , row2 column 1 , x greater than negative 3 , row3 column 1 , y greater than or equal to 1 , end table
49. { y ≤ 2 3 x + 2 y ≥ | x | + 2 left brace . table with 2 rows and 1 column , row1 column 1 , y less than or equal to , 2 thirds , x plus 2 , row2 column 1 , y greater than or equal to vertical line x vertical line plus 2 , end table
50. { y < x − 1 y > − | x − 2 | + 1 left brace . table with 2 rows and 1 column , row1 column 1 , y less than x minus 1 , row2 column 1 , y greater than negative vertical line x minus 2 vertical line plus 1 , end table
51. { 2 x + y ≤ 3 y > | x + 3 | − 2 left brace . table with 2 rows and 1 column , row1 column 1 , 2 x plus y less than or equal to 3 , row2 column 1 , y greater than vertical line x plus 3 vertical line negative 2 , end table
52. { y < | x − 1 | + 2 x ≥ 0 left brace . table with 2 rows and 1 column , row1 column 1 , y less than vertical line x minus 1 vertical line plus 2 , row2 column 1 , x greater than or equal to 0 , end table
53. { y > | x − 1 | + 1 y ≤ − | x − 3 | + 4 left brace . table with 2 rows and 1 column , row1 column 1 , y greater than vertical line x minus 1 vertical line plus 1 , row2 column 1 , y less than or equal to negative vertical line x minus 3 vertical line plus 4 , end table
54. { y ≤ | x | − 2 y ≤ | x | + 2 left brace . table with 2 rows and 1 column , row1 column 1 , y less than or equal to vertical line x vertical line negative 2 , row2 column 1 , y less than or equal to vertical line x vertical line plus 2 , end table

C Challenge

Geometry Write a system of inequalities to describe each shaded figure.

55. 
56. 
57. 
58. 1. Graph the “bowtie” inequality, | y | ≤ | x | . vertical line y vertical line less than or equal to vertical line x vertical line .

    2. Write a system of inequalities to describe the graph shown below.

       

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