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# Systems of linear equations and inequalities pkt. with answers

## by Denise Russell, Coordinator of Special Education Services at Sequel Youth and Family Services on Apr 06, 2013

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## Systems of linear equations and inequalities pkt. with answersDocument Transcript

• Systems of Linear Equations and Inequalities Chapter Questions1. What are the different ways to solve a system of linear equations?2. When do you get an answer to a system of linear equations that has one solution, no solution and infinitely many solutions?3. How is a system of inequalities graphed? Page 1 of 20 www.njctl.org
• Systems of Linear Equations and Inequalities Chapter ProblemsSolve by graphingClasswork1. y = -x – 7 y= x–72. y = - x + 2 y=- x+33. y = -3x – 5 y=x+34. y = -2x + 5 y= x–25. y = -4x + 7 y = -3x + 36. y = x – 3 y= x+27. y = x + 3 y=- x–38. y = x + 2 y = -x – 29. y = 4x – 1 y = -x + 410. y = 3x – 4 y = 4x + 10Homework11. y = - x – 4 y=- +112. y = -2x – 2 y = -3x – 6 Page 2 of 20 www.njctl.org
• 13. y = x – 2 y=x+214. y = x + 1 y=- x–415. y = x – 4 y = -x + 216. y = -4x – 1 y = x – 1117. y = -3x – 3 y= x+418. y = - x + 3 y= x–119. y = -x – 2 y=- x+220. y = x + 5 y = -x + 3Solve by SubstitutionClasswork21. x = 4y – 9 x=y+322. 5x = -2y + 48 x = -3y + 2023. y – 4x = 28 y = -2x – 224. y + 2x = -12 y = x + 1525. x = -2y – 7 2x + y = -1426. x = 5y – 38 x = -4y + 1627. y = 2x + 3 4x – 2y = 8 Page 3 of 20 www.njctl.org
• 28. x = -4y + 8 x = 3y + 829. 5y + 5x = 85 y = 4x – 1830. x = y – 12 x = 5y – 40Homework31. y = -5x + 41 -2x = -14 – 2y32. y = 3x + 6 -6x + 2y = 1233. y – 3x = 0 y = -3x – 1834. x = -3y + 13 4x – 4y = 2035. x = -4y + 29 5x + 2y = 3736. y = -2x + 11 5y – 2x = 3137. 5y – 5x = -15 y = -3x + 2938. -4x = 3y + 32 x = -5y – 839. y = -3x – 1 -4y + x = -940. y = -4x + 17 -3y – x = -7 Page 4 of 20 www.njctl.org
• Solve by Elimination (Addition & Subtraction)Classwork41. 3x + y = 36 5x + y = 5642. x + 2y = 25 x + 3y = 3343. 3x – 5y = -52 x – 5y = -3444. 2x + 3y = 4 -2x + 5y = 6045. 2x + 2y = 2 5x – 2y = 4046. -x + 2y = 14 x – 2y = -1147. 4x – y = 16 4x + 2y = 1648. 2x + 5y = 5 -2x + y = -2349. 2x – 2y = -12 x – 2y = -1350. 5x + 5y = 40 -5x + 3y = -40Homework51. 4x – y = -2 4x + 5y = 1052. 2x + 4y = 10 -4x + 4y = 5253. -3x – 5y = 49 3x + 4y = -4454. -4x + 3y = 39 5x – 3y = -45 Page 5 of 20 www.njctl.org
• 55. -5x – 2y = -5 -x – 2y = -156. x + 5y = -4 -x + 2y = -1057. -4x + 2y = -44 4x + 4y = 2058. x + 2y = 4 x + 5y = -259. 3x – y = -5 -3x – 2y = -1060. 3x – y = 11 -3x – 5y = -71Solve by Elimination (Multiply First)Classwork61. 5x – 4y = 47 -x – 16y = 12562. 3x – 2y = 33 -4x – 4y = 1663. 2x + y = 21 4x + 3y = 5164. -3x + 3y = -27 12x + 5y = 10865. 3x + 4y = 3 -12x – y = -5766. 2x + 5y = -7 8x + 3y = 5767. 4x + 3y = 33 8x + y = 3168. 3x + 3y = 31 -9x – 5y = -6769. –x – y = -8 -4x + 2y = 22 Page 6 of 20 www.njctl.org
• 70. 2x + y = 0 -8x + 4y = 80Solve by Elimination (Multiply First)Homework71. –x + y = -5 -3x + 4y = -1272. -2x – y = 2 -6x + 3y = -1873. -2x + 2y = 16 6x – y = -1374. -4x – 5y = -9 3x + 10y = 1375. 3x – 2y = -26 6x – 4y = -7076. x + 5y = -12 3x + y = 677. x + y = 14 4x – 2y = 278. -3x + 3y = -3 -12x + 5y = -6179. 3x + 2y = 27 -9x + 4y = -5180. 4x + 4y = 20 2x – 16y = -44Choose Your Own StrategyClasswork81. –x + 4y = 5 x + 4y = 1182. 3x – y = 7 4x – 2y = 883. 2y + 5x = 35 y = 4x – 28 Page 7 of 20 www.njctl.org
• 84. 5x – 4y = -39 -3x – 4y = -1585. y = -5x + 59 4x + y = 4986. y = x + 6 y= x+687. -2x + 4y = 28 2x – 3y = -1888. y = -x + 12 3y + 3x = 3689. 2x + 4y = -10 -4x – 12y = 3690. –x – 5y = -3 -2x + 5y = 9Choose Your Own StrategyHomework91. -3x + 5y = -39 12x – 4y = 6092. y = 3x – 18 y – 3x = -2493. x + 3y = 16 -x + 4y = 594. x = -3y – 19 x + 5y = -2295. 3x – 3y = 12 9x + 2y = 10296. y = - x + 4 y = x + 1097. 3x + 2y = 21 -3x + 5y = 2198. –x – y = 7 -x + 5y = 19 Page 8 of 20 www.njctl.org
• 99. 4x + y = -28 -2x + 2y = 24100. x = 2y – 7 -x + 4y = 17Writing Systems to Model SituationsClasswork101. The admission fee at a carnival is \$3.00 for children and \$5.00 for adults. On the first day 1,500 people enter the fair and \$5740 is collected. How many children and how many adults attended the carnival?102. A builder placed two orders with the hardware store. The first order was for 25 sheets of plywood and 4 boxes of nails and the bill totaled \$357. The second order was for 35 sheets of plywood and 2 boxes of nails and the bill totaled \$471. The bills do not list the per-item price. What were the prices of one piece of plywood and one box of nails?Homework103. Two friends bought some markers and pens. The first bought 4 markers and 5 pens and it cost him \$6.71. The second friend bought 5 markers and 3 pens, which cost her \$7.12. What is the price for one marker and one pen?104. The ticket price for the movies is \$7.50 for children and \$10.50 for adults. One night 825 people bought tickets and \$8005.50 was collected from ticket sales. How many children and how many adults bought tickets.Solving Systems of Inequalities by GraphingClasswork105. y x–2 y x+2106. y x–1 y 5x – 5107. y - x–3 y x+3108. y > 2x – 5 3x + 4y < 12109. x+y -3 5x – y -3 Page 9 of 20 www.njctl.org
• Homework110. y x+2 y > 3x – 3111. y -x + 5 y 3x – 4112. y< x y -x + 4113. y > 2x +4 2x – y 4114. 3x – y - 1 x + y -3Unit ReviewMultiple ChoiceChoose the correct answer for each question.1. Solve the system: x - y = -8 x + 3y = 12 a. (-5,3) b. (7,1) c. (6,2) d. (-3,5)2. Solve the system: -x +4y = 12 5x - 2y = -6 a. (-12,0) b. (8,5) c. (0,3) d. (4,4) Page 10 of 20 www.njctl.org
• 3. Solve the system: -3x + y = -7 2x - 5y = 22 a. (0,-7) b. (0,-4.5) c. (1,-4) d. No solution4. What point is the intersection of the graphs of the lines 3x + y = 6 and -3x + y = -6? a. (2,1) b. (0,2) c. (2, 0) d. (3, 3)5. What is true of the graphs of the two lines x = 2y - 6 and x = -3y – 14? a. No solution b. Intersect at (2,4) c. Intersect at (4,2) d. One solution6. What is true of the graphs of the two lines 3x + 4y = 2 and 9x + 12y = 6? a. No solution b. Intersect at (0,.5) c. Intersect at (0,0) d. Infinitely many solutions7. What is true of the graphs of the two lines 3x + 5y = -9 and -6x - 10y = -12? a. No solution b. Intersect at (-3,0) c. Intersect at (2,-5) d. Infinitely many solutions Page 11 of 20 www.njctl.org
• 8. What is the value of y in the following system of equations? x + 5y = 7 x - 3y = –1 a. 1 b. 2 c. -3 d. 49. What is the value of the y-coordinate of the solution to the system of equations - 3 x + y = 9 and x − y = 7? a. 6 b. 2 c. 3 d. -1510. F i v e times as many girls as boys went to the dance. If a total of 120 students went t o the dance, how many were gi rl s ? a. 60 b. 80 c. 100 d. 11011. Which graph represents the following system of inequalities? -x + y < - 1 2x + y ≥ 2 a. b. c. Page 12 of 20 www.njctl.org
• 12. Which of these points is a solution of the system y >- 2x + 3 and -x + y > 0? a. (2,-6) b. (-1,-2) c. (5,2) d. (1,3)13. Which coordinate point is in the solution set for the system of inequalities shown in the accompanying graph? a. (1,3) b. (-1,3) c. (1,–5) d. (-3,0)Short Constructed Response – Write the correct answer for each question.14. Sketch a graph of a system that has infinitely many solutions.15. Sketch a graph of a system that has no solution.16. The el em ent ary sc ho ol st u de nt s a re put t i n g on a pl ay a s a f un drai ser. T h e st ud ent t i ck et s co s t \$2. 0 0 eac h a nd t he ad ul t t i cket s c o st \$4 eac h. T h e y sol d 5 t i m es a s m any st ud ent t i ck et s a s a dul t t i ck et s. T hey m ad e \$ 14 0. H o w m an y st u de nt a nd ad u l t t i cket s were sol d ? Page 13 of 20 www.njctl.org
• 17. Write the system of inequalities graphed belowExtended Constructed Response - Solve the problem, showing all work.18. Telephone company A charges \$20 per month and \$0.10 per text. Telephone company B charges \$15 per month and \$0.20 per text. Let t = the number of texts and C = cost. a. Write an equation to represent the cost of each plan. b. Solve the system by graphing. c. Explain what the solution to the system means in terms of what telephone company to provide services. Page 14 of 20 www.njctl.org
• Answer Key1. x=0, y=-72. x=4, y=13. x=-2, y=14. x=3, y=-15. x=4, y=-96. No solution7. x=-3, y=-18. x=-3, y=19. x=1, y=310. x=-14, y=-4611. x=-5, y=3.512. x=-4, y=613. No solution14. x=-4, y=-215. x=3, y=-116. x=2, y=-917. x=-2, y=318. x=5, y=119. x=-8, y=620. x=-1, y=421. x=7, y=422. x=8, y=423. x=-5, y=824. x=-9, y=625. x=-7, y=026. x=-8, y=627. No solution28. x=8, y=029. x=7, y=1030. x=-5, y=731. x=8, y=132. Same function33. x=-3, y=-934. x=7, y=-235. x=5, y=636. x=2, y=737. x=8, y=538. x=-8, y=039. x=-1, y=240. x=4, y=141. x=10, y=642. x=9, y=843. x=-9, y=544. x=-10, y=845. x=6, y=-546. No solution47. x=4, y=048. x=10, y=-349. x=1, y=750. x=8, y=051. x=0, y=252. x=19, y=-753. x=8, y=-554. x=-6, y=21 Page 15 of 20 www.njctl.org
• 55. x=-1, y=056. x=6, y=-257. x=9, y=-458. x=8, y=-259. x=0, y=560. x=7, y=1061. x=3, y=-862. x=5, y=-963. x=6, y=964. x=9, y=065. x=5, y=-366. x=9, y=-567. x=3, y=768. x=23/6, y=13/269. x=-1, y=970. x=-5, y=1071. x=8, y=372. x=1, y=-473. x=-1, y=774. x=1, y=175. No solution76. x=3, y=-377. x=5, y=978. x=8, y=779. x=7, y=380. x=2, y=381. x=3, y=282. x=3, y=283. x=7, y=084. x=-3, y=685. x=10, y=986. x=0, y=687. x=6, y=1088. x=0, y=1289. x=3, y=-490. x=-2, y=191. x=3, y=-692. No solution93. x=7, y=394. x=-14.5, y=-1.595. x=10, y=696. x=-3, y=897. x=3, y=698. x=-9, y=299. x=-8, y=4100. x=3, y=5101. Adults: 620, Children: 880102. Plywood: \$13, Box of nails: \$8103. Pen: \$0.39, Marker: \$1.19104. Children: 219, Adults 606 Page 16 of 20 www.njctl.org
• 105.106.107. Page 17 of 20 www.njctl.org
• 108.109.110. Page 18 of 20 www.njctl.org
• 111.112.113. Page 19 of 20 www.njctl.org
• (Parallel Lines)114.Review Answers 1. D 6. D 11. A 15. Answers 2. C 7. A 12. D vary 3. C 8. A 13. D 16. 10 adults 4. C 9. D 14. Answers and 50 5. D 10. C vary students 17. y>-x y≥ x–6 18. a. C = .10t + 20 C = .20t + 15 b. c. The plans cost the same with 50 text messages. Page 20 of 20 www.njctl.org