Answers (Lesson 31) Answers. Skills Practice. Practice (Average)


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1 Glencoe/McGrawHill A3 Glencoe Algebra 3 NAME DATE PERID Solving Sstems of Equations B Graphing Solve each sstem of equations b graphing (, 0) 4 (, 0) (, ) (3, ) 5 3 (3, 4) 3 4 (, ) (3, ) (, ) 5 8 (4, 0) (, 5) Graph each sstem of equations and describe it as consistent and independent, consistent and dependent, or inconsistent (, 0) (, ) (3, 4) inconsistent consistent and consistent and dependent independent Glencoe/McGrawHill Glencoe Algebra (4, 0) (, 0) (, 5) (, ) (, ) (5, 0) Lesson 33 Solve each sstem of equations b graphing (, ) 3 (, ) 9 (3, 3) (, ) (, ) 6 4 (, ) (, ) NAME DATE PERID Solving Sstems of Equations B Graphing Graph each sstem of equations and describe it as consistent and independent, consistent and dependent, or inconsistent (, ) (, 0) consistent and indep. inconsistent consistent and dep. SFTWARE For Eercises 0, use the following information. Location Mapping needs new software. Software A costs $3,000 plus $500 per additional site license. Software B costs $500 plus $00 per additional site license. 0. Write two equations that represent the cost of each software. A: 3, , B: Graph the equations. Estimate the breakeven point of the software costs. 5 additional licenses. If Location Mapping plans to bu 0 additional site licenses, which software will cost less? B Software Costs (5, 0,500) Glencoe/McGrawHill Glencoe Algebra (, ) (, ) Total Cost ($) 4,000 0,000 6,000,000 8,000 4,000 A (3, 3) B (, ) Additional Licenses (Lesson 3)
2 Glencoe/McGrawHill A6 Glencoe Algebra 3 NAME DATE PERID Solving Sstems of Equations Algebraicall Solve each sstem of equations b using substitution.. m n w z m n 4 (8, ) (3, ) w 3z (3, ) 4. 3r s 5 5. b 3c 4 6. r s 5 (, ) b c 3 (3, 0) 3 (3, ) Solve each sstem of equations b using elimination. 7. p q 5 8. j k c d 3p q 5 (, ) 3j k (, ) 3c 4d 50 (6, 8) 0. f 3g 9.. f g (3, ) 3 (, ) 6 no solution Solve each sstem of equations b using either substitution or elimination. 3. r t r t 4 (, 6) 4,4 (3, 5) 6. p 3q w 8z 6 8. c d 6 p 3q 6 (3, 0) 3w 4z 8 c d 0 (3, 3) infinitel man 9. u 4v a b. 6 u v 3 no solution 3a b 5 (, ) 3 6 (4, ). 3 z 6 3. c d 4. 3r s 3 z 6 (, 0) c 5d 3 ( 4, ) r 3s 9 ( 3, 5) 5. The sum of two numbers is. The difference of the same two numbers is 4. Find the numbers. 4, 8 6. Twice a number minus a second number is. Twice the second number added to three times the first number is 9. Find the two numbers., 3 Glencoe/McGrawHill 7 Glencoe Algebra Lesson 33 NAME DATE PERID Solving Sstems of Equations Algebraicall Solve each sstem of equations b using substitution g 3h 8 no 3 (7, 0) (3, ) g h 9 3 solution 4. a 4b 6 infinitel 5. m n a b 3 man 5m 6n (5, 4) 7 ( 3, ) 7. u v w 3z u v 5 no solution 4 9 (, 5) 3w 5z 4, Solve each sstem of equations b using elimination. 0. r s 5. m n r s 0 (5, 5) 3m n 30 (4, 9) 8 5 (, 4) 3. 3j k no 5. g h 6 4j k 6 (6, 8) 4 6 solution 3g h 6 (4, ) 6. t 4v 6 infinitel t v 3 man 4 (6, 3) (4, 3) Solve each sstem of equations b using either substitution or elimination q 5r infinitel , 3 4q r 56 (0, 8) man. 4b d 5 no 3. s m p 0 b d solution s (, ) 3m 9p 5, 5. 5g 4k h z 3 no 3g 5k 7 (6, 5) 8 (, 3) 3h 3z 6 solution SPRTS For Eercises 8 and 9, use the following information. Last ear the volleball team paid $5 per pair for socks and $7 per pair for shorts on a total purchase of $35. This ear the spent $34 to bu the same number of pairs of socks and shorts because the socks now cost $6 a pair and the shorts cost $8. 8. Write a sstem of two equations that represents the number of pairs of socks and shorts bought each ear , How man pairs of socks and shorts did the team bu each ear? socks:, shorts: 5 Glencoe/McGrawHill 8 Glencoe Algebra 3 3 (Lesson 3)
3 Glencoe/McGrawHill A9 Glencoe Algebra 33 NAME DATE PERID Solving Sstems of Inequalities b Graphing Solve each sstem of inequalities b graphing no solution Find the coordinates of the vertices of the figure formed b each sstem of inequalities (, 4), (0, 0), (0, ), (, 0) (0, 3), ( 5, 3), ( 5, 8) (, 4), (, 0) Glencoe/McGrawHill 33 Glencoe Algebra Lesson NAME DATE PERID Solving Sstems of Inequalities b Graphing Solve each sstem of inequalities b graphing Find the coordinates of the vertices of the figure formed b each sstem of inequalities (, 0), (3, ), (3, ) (, 4), (, 4), (, 0) 3 ( 3, 4),,, (3,4) DRAMA For Eercises 0 and, use the following information. The drama club is selling tickets to its pla. An adult ticket costs $5 and a student ticket costs $. The auditorium will 400 seat 300 ticketholders. The drama club wants to collect at 350 least $3630 from ticket sales 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. 0, 0, 300, List three different combinations of tickets sold that satisf the inequalities. Sample answer: 50 adult and 50 student, 00 adult and 00 student, 45 adult and 48 student Pla Tickets Adult Tickets Glencoe/McGrawHill 34 Glencoe Algebra Student Tickets (Lesson 33)
4 Glencoe/McGrawHill A Glencoe Algebra 34 NAME DATE PERID Linear Programming Graph each sstem of inequalities. Name the coordinates of the vertices of the feasible region. Find the maimum and minimum values of the given function for this region f(, ) f(, ) 3 f(, ) ma.: 9, min.: 3 ma.:, min.: 5 ma.:, min.: f(, ) 6 4 f(, ) 4 3 f(, ) 3 5 (, 7) (, 4) (5, 4) (, ) (5, ) (, 6) (, ) (, ) ma.: 3, no min. no ma., min.: 0 ma.:, min.: 7. MANUFACTURING A backpack manufacturer produces an internal frame pack and an eternal frame pack. Let represent the number of internal frame packs produced in one hour and let represent the number of eternal frame packs produced in one hour. Then the inequalities 3 8, 6, 0, and 0 describe the constraints for manufacturing both packs. Use the profit function f() and the constraints given to determine the maimum profit for manufacturing both backpacks for the given constraints. $60 Glencoe/McGrawHill 39 Glencoe Algebra (, 4) (3, 6) (8, 6) ( 3, ) (0, 7) (0, 0) (7, 0) (, 5) Lesson NAME DATE PERID Linear Programming Graph each sstem of inequalities. Name the coordinates of the vertices of the feasible region. Find the maimum and minimum values of the given function for this region f(, ) f(, ) f(, ) 3 (4, 5) ( 3, ) (3, ) (3, 6) (0, 6) (0, 4) ma.: 8, min.: 4 ma.:, min.: 6 ma.: 5, min.: f(, ) 4 f(, ) 3 0 f(, ) 4 3 ( 7 4, 0) (0, 0) (0, 7) (, 0) (0, 3) 34 7 ma.: 8, min.: 0 ma.:, no min. no ma., min.: 5 PRDUCTIN For Eercises 7 9, use the following information. A glass blower can form 8 simple vases or elaborate vases in an hour. In a work shift of no more than 8 hours, the worker must form at least 40 vases. 7. Let s represent the hours forming simple vases and e the hours forming elaborate vases. Write a sstem of inequalities involving the time spent on each tpe of vase. s 0, e 0, s e 8, 8s e If the glass blower makes a profit of $30 per hour worked on the simple vases and $35 per hour worked on the elaborate vases, write a function for the total profit on the vases. f(s, e) 30s 35e 9. Find the number of hours the worker should spend on each tpe of vase to maimize profit. What is that profit? 4 h on each; $60 Glencoe/McGrawHill 40 Glencoe Algebra (, ) ( 7 5, 9 5 ) (0, 0) (0, ) ( 3, ) (5, 0) (Lesson 34)
5 Glencoe/McGrawHill A5 Glencoe Algebra 35 NAME DATE PERID Solving Sstems of Equations in Three Variables Solve each sstem of equations.. a c 0 (5, 5, 0). z 3 (0,, ) b c 5 3 z a b c 5 5z z 6 ( 3,, ) 4. 4 z no solution z 0 z 4 z 0 5. z 6 (,, 3) 6. 3 z (,, 3) 3 z 6 z 3z z 5 (0, 0, ) 8. 3r t (, 6, ) 3 0 4r s t 6 3 z r s 4t z 3 no solution 0. 5m 3n p 4 (, 3, 5) 6z 6 3m n 0 5z 3 m n 3p 8. z infinitel man. z 4 (,, ) 3 z 4 3 z 3 z 3 z z (5, 7, 0) z infinitel man z 4 z 8 5 0z z 5. 3z (, 3, ) z 0 (3, 0, ) z 3 5z 3 3 3z 5 3 z 9 7. z (,, 3) 8. z infinitel man 3 3 z 0 z 6 z 3 6 6z 3 9. The sum of three numbers is 8. The sum of the first and second numbers is 5, and the first number is 3 times the third number. Find the numbers. 9, 6, 3 Glencoe/McGrawHill 45 Glencoe Algebra Lesson NAME DATE PERID Solving Sstems of Equations in Three Variables Solve each sstem of equations.. z z 7 3. a b 3 z 3 3z b c 3 3 z 8 4z 6 a c 0 (3,, 5) (,4, 4) (,, 4) 4. 3m n 4p 5 5. g 3h 8j 0 6. z 8 m n p 3 g 4h 4 z 3 m 4n 5p 0 g 3h 8j 5 3 z 5 (3, 3, 3) no solution (, 3, ) 7. 5 z z 9. p 4r 7 3 z 7 5 3z 0 p 3q z 7 5 z 4 q r (5,, 0) (,, ) (, 3, ) z 8. d 3e f z z 0 d e f 4 z z 4 4d e f 3 z infinitel man (,, ) (, 3, 4) z z z 0 z 3 4z 5 5 z 7 5 z 6 3 9z 9 3 3z 9 ( 7, 6, ) infinitel man (, 3, ) 6. u v w z 8 8. z 3u v 3w 7 3 5z z 6 u v w 7 3 8z 8 4 z (0,, 3) (,, 3) no solution 9. 4z 0. 9z z z 3 4 z 4 0 z 6 3 z z z 9 (4, 5, 0) (,, 3) (,, 5). The sum of three numbers is 6. The third number is the sum of the first and second numbers. The first number is one more than the third number. Find the numbers. 4,, 3 3. The sum of three numbers is 4. The second number decreased b the third is equal to the first. The sum of the first and second numbers is 5. Find the numbers. 3,, 4. SPRTS Aleandria High School scored 37 points in a football game. Si points are awarded for each touchdown. After each touchdown, the team can earn one point for the etra kick or two points for a point conversion. The team scored one fewer point conversions than etra kicks. The team scored 0 times during the game. How man touchdowns were made during the game? 5 Glencoe/McGrawHill 46 Glencoe Algebra (Lesson 35)
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