3-2 Study Guide and Intervention

Transcription

1 NAME DATE PERID 3-2 Stud Guide and Intervention Solving Sstems of Inequalities b Graphing Sstems of Inequalities To solve a sstem of inequalities, graph the inequalities in the same coordinate plane. The solution of the sstem is the region shaded for all of the inequalities. Eample Solve the sstem of inequalities. 2-1 and > The solution of 2-1 is Regions 1 and 2. The solution of > + 2 is Regions 1 and 3. 3 The intersection of these regions is Region 1, which is the solution set of the sstem of inequalities. Eercises Solve each sstem of inequalities b graphing. 6 Region Region Region > < < 2 < < < > > < -4 Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 12 Glencoe Algebra 2

2 NAME DATE PERID 3-2 Stud Guide and Intervention (continued) Solving Sstems of Inequalities b Graphing Find Vertices of an Enclosed Region Sometimes the graph of a sstem of inequalities produces an enclosed region in the form of a polgon. You can find the vertices of the region b a combination of the methods used earlier in this chapter: graphing, substitution, and/or elimination. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Eample Find the coordinates of the vertices of the triangle formed b + 4 < 20, < 2 + 3, and - 3 < 4. Graph each inequalit. The intersections of the boundar lines are the vertices of a triangle. The verte (4, 0) can be determined from the graph. To find the coordinates of the second and third vertices, solve the two sstems of equations = = and + 4 = 20-3 = 4 For the first sstem of equations, rewrite the first equation in standard form as 2 - = -3. Then multipl that equation b 4 and add to the second equation. 2 - = -3 Multipl b = = 20 (+) + 4 = = 8 8 = 13 Then substitute = 8 in one of the original equations 13 and solve for. 2 ( 8 13 ) - = = -3 = 13 The coordinates of the second verte are ( 8 13, 4 13) For the second sstem of equations, use substitution. Substitute for in the second equation to get - 3(2 + 3) = = 4 - = 13 = - 13 Then substitute = - 13 in the first equation to solve for. = 2 ( - 13 ) + 3 = = - 11 The coordinates of the third verte are ( -2 3, -2 1 ). Thus, the coordinates of the three vertices are (4, 0), ( 8 13, 4 13) 3 and ( -2 3, -2 1 ). Eercises Find the coordinates of the vertices of the triangle formed b each sstem of inequalities > < < 1 2 < > > -2 > - 1 < Lesson 3-2 Chapter 3 13 Glencoe Algebra 2

3 NAME DATE PERID 3-2 Skills Practice Solving Sstems of Inequalities b Graphing Solve each sstem of inequalities b graphing. 1. < > < < 3 8. < < < 4 Find the coordinates of the vertices of the triangle formed b each sstem of inequalities Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 14 Glencoe Algebra 2

4 NAME DATE PERID 3-2 Practice Solving Sstems of Inequalities b Graphing Solve each sstem of inequalities b graphing < - 2. > > > < > -6 Lesson 3-2 Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Find the coordinates of the vertices of the triangle formed b each sstem of inequalities < DRAMA The drama club is selling tickets to its pla. An adult ticket costs $1 and a student ticket costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least $3630 from ticket sales. 400 a. Write and graph a sstem of four inequalities that describe how man of each tpe of ticket the club must sell to meets its goal. b. List three different combinations of tickets sold that satisf the inequalities. Student Tickets Pla Tickets Adult Tickets Chapter 3 1 Glencoe Algebra 2

5 NAME DATE PERID 3-2 Word Problem Practice Solving Sstems of Inequalities b Graphing 1. BIRD BATH Melissa wants to put a bird bath in her ard at point (, ), and wants it to be inside the enclosed shaded area shown in the graph. 4. DECK The Wrights are building a deck. The deck is defined b the inequalities, ,, and Graph the inequalities and find the coordinates of the deck s corners. - First, she checks that -3 and -2. What linear inequalit must she check to conclude that (, ) is inside the triangle? 2. SQUARES Matt finds a blot of ink covering his writing in his notes for math class. He sees A square is defined b 8 and _. Write an inequalit that completes this sentence. A square is defined b 8 and 3. HLIDAY Amanda received presents and cards from friends over the holida season. Ever present came with one card and none of her friends sent her more than one card. Less than 10 of her friends sent onl a card. Describe this situation using inequalities.. TICKETS The auditorium at McCaske East High School in Lancaster, PA has 800 seats. Suppose that the drama club has a goal of making $3400 each night of their spring pla to cover epenses and raise mone for the club. Adult tickets are $7 and student/senior tickets are $4. a. Write a sstem of inequalities for the number of seats and the mone raised b the drama club. b. Graph the inequalities on the graph below. Adult Tickets Student/Senior Tickets c. Could the club meet its goal b selling 200 adult and 47 student/senior tickets? Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 16 Glencoe Algebra 2

6 NAME DATE PERID 3-2 Enrichment Creative Designs A sstem of linear inequalities can be used to define the region bounded b a geometric shape graphed on a coordinate plane. For eample, the rectangle shown can be defined b the sstem 4, 0, 3, and 0. The triangle shown can be described using the inequalities + 2 4, 0, and 1. Lesson 3-2 Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 1. Find a sstem of linear inequalities to describe the area bounded b the bow tie shape below. The intersection points are (1, 1), (1, 4), (3, 3), (, 2), and (, ). 2. Find a sstem of linear inequalities to describe the area bounded b the basic house shape shown below. The intersection points are (1,1), (1,), (3,7), (,), and (,1). Chapter 3 17 Glencoe Algebra 2