Berkeley City College Precalculus - Math 1 - Chapter 11. Name

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1 Berkele Cit College Precalculus - Math 1 - Chapter 11 Homework 7 Due: Sstems of Equations Name Verif that the values of the variables listed are solutions of the sstem of equations. 1) 3 + = = 1) = -3, = - Objective: (11.1) Solve Sstems of Equations b Substitution Solve the sstem of equations b substitution. ) = = 0 ) Objective: (11.1) Solve Sstems of Equations b Substitution Solve the sstem of equations b elimination. 3) + 3 = 1 - = 38 Objective: (11.1) Solve Sstems of Equations b Elimination 3) ) = + = 11 9 Objective: (11.1) Solve Sstems of Equations b Elimination ) Instructor: K. Pernell 1

2 Solve the sstem of equations. [Hint: Let u = 1 and v = 1, and solve for u and v. Then let = 1 u, and = 1 v.] ) + = = Objective: (11.1) Solve Sstems of Equations b Elimination ) Solve the problem. ) A flat rectangular piece of aluminum has a perimeter of inches. The length is 1 inches longer than the width. Find the width. Objective: (11.1) Solve Sstems of Equations b Elimination ) 7) The Famil Fine Arts Center charges $ per adult and $1 per senior citizen for its performances. On a recent weekend evening when 7 people paid admission, the total receipts were $833. How man who paid were senior citizens? Objective: (11.1) Solve Sstems of Equations b Elimination 7) 8) The perimeter of a parking lot is 00 ards. Find the dimensions of the lot if the length is 0 ards more than three times the width. Objective: (11.1) Solve Sstems of Equations b Elimination 8) 9) A store has a sale on workout gear. Mark bought three pairs of shorts and three T -shirts for $70.3 (before ta). Later, he went back and bought two more pairs of shorts and four more T-shirts for $3.90 (before ta). How much did the shorts and T-shirts cost? Objective: (11.1) Solve Sstems of Equations b Elimination 9)

3 Solve the sstem of equations. If the sstem has no solution, sa that it is inconsistent. ) - = = -17 Objective: (11.1) Identif Inconsistent Sstems of Equations Containing Two Variables ) 11) + = + 0 = Objective: (11.1) Epress the Solution of a Sstem of Dependent Equations Containing Two Variables 11) 1) + = =-3 Objective: (11.1) Epress the Solution of a Sstem of Dependent Equations Containing Two Variables 1) Verif that the values of the variables listed are solutions of the sstem of equations. 13) + + z = z = z = 11 13) =, =, z = 1 Objective: (11.1) Solve Sstems of Three Equations Containing Three Variables 1) - + z = 18 + z = + + z = 9 = 0, =, z = Objective: (11.1) Solve Sstems of Three Equations Containing Three Variables 1) 3

4 Solve the sstem of equations. 1) + + z = z = 19 z = Objective: (11.1) Solve Sstems of Three Equations Containing Three Variables 1) 1) + + z = z = + + 3z = -11 Objective: (11.1) Solve Sstems of Three Equations Containing Three Variables 1) Solve the problem. 17) The Famil Arts Center charges $1 for adults, $17 for senior citizens, and $ for children under 1 for their live performances on Sunda afternoon. This past Sunda, the paid revenue was $1,001 for 8 tickets sold. There were 8 more children than adults. How man children attended? Objective: (11.1) Solve Sstems of Three Equations Containing Three Variables 17) 18) Ron attends a cocktail part (with his graphing calculator in his pocket). He wants to limit his food intake to 13 g protein, 17 g fat, and 19 g carbohdrate. According to the health conscious hostess, the marinated mushroom caps have 3 g protein, g fat, and 9 g carbohdrate; the spic meatballs have 1 g protein, 7 g fat, and 1 g carbohdrate; and the deviled eggs have 13 g protein, 1 g fat, and g carbohdrate. How man of each snack can he eat to obtain his goal? Objective: (11.1) Solve Sstems of Three Equations Containing Three Variables 18) Solve the sstem of equations. If the sstem has no solution, sa that it is inconsistent. 19) + + z = z =- + + z =- Objective: (11.1) Identif Inconsistent Sstems of Equations Containing Three Variables 19)

5 Solve the sstem of equations. 0) z = z = z =- Objective: (11.1) Epress the Solutions of a Sstem of Dependent Equations Containing Three Variables 0) 1) - + z = z =- - + z =- Objective: (11.1) Epress the Solutions of a Sstem of Dependent Equations Containing Three Variables 1) The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the sstems of equations. Are the points of intersection solutions to the sstem of equations (Y/N)? ) ) 7 (3, ) 3 (-, 0) = + = Objective: (11.) Solve a Sstem of Nonlinear Equations Using Substitution

6 Graph the equations of the sstem. Then solve the sstem to find the points of intersection. 3) = = - + 3) Objective: (11.) Solve a Sstem of Nonlinear Equations Using Substitution ) + = 1 = - ) Objective: (11.) Solve a Sstem of Nonlinear Equations Using Substitution

7 ) = = - ) Objective: (11.) Solve a Sstem of Nonlinear Equations Using Substitution Solve the sstem of equations using substitution. ) = + = - ) Objective: (11.) Solve a Sstem of Nonlinear Equations Using Substitution 7) ln = 3ln 3 = 7 Objective: (11.) Solve a Sstem of Nonlinear Equations Using Substitution 7) Solve using elimination. 8) + = 1 - = 17 Objective: (11.) Solve a Sstem of Nonlinear Equations Using Elimination 8) 7

8 9) 3-3 = -1 + = Objective: (11.) Solve a Sstem of Nonlinear Equations Using Elimination 9) Solve the problem. 30) Find the dimensions of a rectangle whose perimeter is 38 feet and whose area is 0 square feet. Objective: (11.) Solve a Sstem of Nonlinear Equations Using Elimination 30) Graph the inequalit. 31) > 31) Objective: (11.7) Graph an Inequalit 8

9 3) -7 3) Objective: (11.7) Graph an Inequalit 33) + 33) - - Objective: (11.7) Graph an Inequalit 9

10 3) + < 3) Objective: (11.7) Graph an Inequalit 3) + 3 3) Objective: (11.7) Graph an Inequalit

11 3) + > 9 3) Objective: (11.7) Graph an Inequalit 37) > + 37) A) B) C) D) Objective: (11.7) Graph an Inequalit 11

12 38) 38) A) B) C) D) Objective: (11.7) Graph an Inequalit 1

13 Graph the sstem of inequalities. 39) > 39) Objective: (11.7) Graph a Sstem of Inequalities 0) + > 8 + < 1 0) Objective: (11.7) Graph a Sstem of Inequalities 13

14 1) -3 + < > 1 8 1) Objective: (11.7) Graph a Sstem of Inequalities ) ) Objective: (11.7) Graph a Sstem of Inequalities 1

15 3) ) Objective: (11.7) Graph a Sstem of Inequalities 1

16 ) ) A) B) C) D) Objective: (11.7) Graph a Sstem of Inequalities 1

17 ) > + 30 ) A) B) C) D) Objective: (11.7) Graph a Sstem of Inequalities 17

18 Answer Ke Testname: MATH1_CH11_HW_7 1) not a solution ) = 0, = -7; (0, -7) 3) =, = -3; (, -3) ) = 18, = 1 ; 18, 1 ) = 1, = -8; 1, -8 ) 8 in. 7) 39 senior citizens 8) 00 d b 0 d 9) shorts: $1.9; T-shirts: $8.0 ) inconsistent 11) = - +, where is an real number or {(, ) = - +, where is an real number} 1) = - + 7, where is an real number or {(, ) = - + 7, where is an real number} 13) not a solution 1) solution 1) = 3, = -, z = ; (3, -, ) 1) = 1, = -1, z = -; (1, -1, -) 17) 303 children 18) 9 mushrooms, meatballs, eggs 19) inconsistent 0) = z +, and = - z, where z is an real number or {(,, z) = z +, and = - z, where z is an real number} 1) = -3 - z, and = 3z + 1, where z is an real number or {(,, z) = -3 - z, and = 3z + 1, where z is an real number} ) No 3) (, ), (, 1) 18

19 Answer Ke Testname: MATH1_CH11_HW_7 ) (0, -), ( 7, 3), (- 7, 3) ) (, ) ) = -, = -3; = -3, = - or (-, -3), (-3, -) 7) = 3 3, = 3 or (3 3, 3) 8) = 9, = 8; = -9, = 8; = 9, = -8; = -9, = -8 or (9, 8), (-9, 8), (9, -8), (-9, -8) 9) =, = 3; = -, = 3 ; =, = -3; = -, = -3 or (, 3), (-, 3), (, -3), (-, -3) 30) ft b 1 ft 31)

20 Answer Ke Testname: MATH1_CH11_HW_7 3) ) - - 3)

21 Answer Ke Testname: MATH1_CH11_HW_7 3) ) ) B 38) A 39)

22 Answer Ke Testname: MATH1_CH11_HW_7 0) No solution ) )

23 Answer Ke Testname: MATH1_CH11_HW_7 3) ) B ) B 3

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Math 1 Final Eam Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve. 1) - - 6 = - + 7 1) ) 6 + 7(- - ) = -8 - ) ) - t + t = 6 t + 1 ) Solve