5.2 Start Thinking Sample answer: x the cost of an incandescent light bulb, y the cost of a CFL, 30x 2 3 3, t 25; t 6F

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1 5.1 Cumulative Review Warm Up. y y 1. y y y y 5 7. y y Practice A yes. no., 0 4., 4 5., 6 6., , , bracelets, 1 necklaces 10. y 4 4, y 6 6; 5, 4 ; When 5, the rectangles have the same area (4 square units). 5.1 Practice B 1. 0,., 1. 4, 4., 5. 4, 6. 1, , , pencils, pens 10. a. y 10 90, y Puzzle Time THE DOORBELL 5. Start Thinking Sample answer: the cost of an incandescent light bulb, y the cost of a CFL, 0 0y 40., 0 0y 4.; y y Warm Up.015, 1... w 4 4. a a 5. Cumulative Review Warm Up t 5; t 6F w; w 5. ft. b ; b $ Practice A 1. Sample answer: Solve either equation for y; The coefficient is 1.. Sample answer: Solve the second equation for. The coefficient is 1.. Sample answer: Solve the first equation for y; The coefficient is 1. 4., ,1 6., 7. 10, 8. 4, 6 9., 1 b. no; The intersection point of the two lines is 11, 00, so you will both have the same amount of money ($00) in your savings accounts after 11 weeks. 5.1 Enrichment and Etension 1. 1,. 9, 5. 1, 4. 0, and 10. In Step 1, you must solve for, not ; Step 1: 4y 9; 4y 9; 4y 9; Step : 4y 9 y 7; 1y 7 y 7; 10y 0; y 11. Sample answer: y 5, y 4 1. Sample answer: y 1, y 9 1. Sample answer: y, 4 9y a. 9 multiple choice, 7 essay b. no; The product of 9 4 is 116, which is greater than 100. Copyright Big Ideas Learning, LLC Algebra 1 A51

2 15. a, b 4 5. Practice B 1. 5,.,1. 9, , , , 7 7. y 7, y 10; 1 dogs, 5 cats 8. Sample answer: y 8, 5y 9. Sample answer: y 18, y Sample answer:, y small lanterns and 1 large lanterns 1. a. y 60 b. 60, y a. y b. 7, y Sample answer: equation 1: y 5, equation : y Enrichment and Etension 1. 0, 5, 4. 0,, 5., 0, 4. 1,, 5., 5, 6 5. Puzzle Time HE MADE A KNOT IN HIS TAIL AND CALLED IT A PIG S TIE 5. Start Thinking yes; The coefficients of the y-values in each equation are both ; 6; This method allows you to eliminate one variable, leaving a simple equation to be solved for the remaining variable; ; Like the substitution method learned in Section 5., from this point, substitute the -value back into one of the y 1;,1 original equations to obtain 5. Warm Up y. 7a 4. 9y Cumulative Review Warm Up 1. n 1 5; n 4 or n 6. n 4 8; 4 n 1. n 15 4; n or n 8 4. n 9; n 5. Practice A 1. 5,1.,. 4, 4. 4, 5 5., 1 6., 7., 9 8., 9. 1, 10. 5, , 1 1., 0 1. $0, y $ ,1 ; Sample answer: elimination; Both equations have term. 15., 7 ; Sample answer: substitution; Equation is already solved for y , ; Sample answer: elimination; It is not easy to isolate one variable. 17. a. 4 b. y, 11 y 45 c. 16, y 18, so 16 medium T-shirts, 18 large T-shirts d. 5 medium and 5 large; The number of medium and large shirts already ordered is about the same. 5. Practice B 1., 4., 4., 4., 5. 10, ,1 7. 5, , , 5 10., 1 11., 1. 6, 4 A5 Algebra 1 Copyright Big Ideas Learning, LLC

3 1. subtracted some terms but added others in step ; Step 1 4 5y 10 4y 9 Step Multiply by. 4 5y y 18 1y 8 8 y , ; Sample answer: substitution; = equation 1 15., ; Sample answer: elimination; can get opposite coefficients 1 16., 1 ; Sample answer: elimination; can get opposite coefficients 17. you: 17.5 L; your friend: 1.5 L 5. Enrichment and Etension 1.,. line m: y 1, line : y. use substitution to prove: line m: y, line : y 5., 6., 7. It is a solution to both linear equations. (point of intersection) 8. Shade: 9. y 1, y 10. Sample answer: 1, 1 5. Puzzle Time PLEASE SPARE US 5.4 Start Thinking y, y 5; The slope for each line is the same, ; no; A system of linear equations will intersect at one point when their slopes are different; A system of linear equations will not intersect when they have the same slope, but different y-intercepts. 5.4 Warm Up 1. y 4. y 10. y y 5. y y Cumulative Review Warm Up 1. The graph of g is a vertical translation 4 units up of the graph of f.. The graph of g is a vertical translation 1 unit down of the graph of f.. The graph of g is a horizontal translation 6 units rights of the graph of f. 5.4 Practice A 1. B; no solution. A; one solution. C; infinitely many solutions 4. no solution 5. 0, 7 6. infinitely many solutions 7. infinitely many solutions; same slope and same y-intercept Copyright Big Ideas Learning, LLC Algebra 1 A5

4 8. no solution; same slope and different y-intercepts 9. one solution; different slopes 10. Equation is y 5 in slope-intercept form; y 5; y 5; The lines have the same slope and the same y-intercept, So, the system has infinitely many solutions y 18, 15y 7; no; Equation is a multiple of equation 1, so there are infinitely many solutions. 5.4 Practice B 1. B; infinitely many solutions. A; one solution. C; no solution 4. infinitely many solutions 5. no solution 6. 1, 4 7. no solution 8. no solution 9. infinitely many solutions 10. one solution; different slopes 11. infinitely many solutions; same slope and same y-intercept 1. infinitely many solutions; same slope and same y-intercept 1. no solution; same slope but different y-intercepts 14. one solution; different slopes 15. infinitely many solutions; same slope and same y-intercept 16. Sample answer: y, y 6, y a. Sample answer: a 1 b. Sample answer: a 5.4 Enrichment and Etension 1. Sample answer: Represent the number of pieces of red, blue, green, and yellow candy by r, b, g, and y. Let t r b g y be the total number of pieces of candy. r t 16 b g y t 16 t 16 t 18 t r b g y. Sample answer: The red, blue, and green equations are the total t minus 16, and the yellow equation is the total t minus 18. The red, blue, and green are all equal.. r 6, b 6, g 6, y 4, t 4. Sample answer: r b g y Add the first four 4t 66 equations from Eercise 1. t 4t 66 Substitute t r b g y for the left side. t 66 Subtraction Property t of Equality Simplify. r b g Substitute t to 6 6 find the remaining values. y Sample answers: yes; yes 6. Sample answer: Solve the system. b g y 16, r g y 16, r b y 16, r b g Puzzle Time A TABLE 5.5 Start Thinking The system of equations is: y 5 18,000, y 59.99, 70.; 71 days A54 Algebra 1 Copyright Big Ideas Learning, LLC

5 5.5 Warm Up Cumulative Review Warm Up 1. 15, 7, 9. 1, 5, 5.5 Practice A no solution. 8. infinitely many solutions 9. 1 and and and games 5.5 Practice B infinitely many solutions infinitely many solutions 8. no solution and a. Sample answer: a, b 1 b. a, b c. Sample answer: a 1, b mi Copyright Big Ideas Learning, LLC Algebra 1 A55

6 5.5 Enrichment and Etension 1..., , ; ; Because only equals negative at zero, algebraically, can be all real numbers greater than or equal to 0. You need the graphical representation to confirm a solution. A56 Algebra 1 Copyright Big Ideas Learning, LLC

7 5.. y 7 r 4. s r t 5. y 11 6 k 6. C Practice A 1. no. yes. yes 4. no 0; Because only equals negative at zero, algebraically, can be all real numbers less than or equal to 0. You need the graphical representation to confirm a solution. 5. no 6. yes 7. yes 8. yes 9. yes 10. no 11. no; The total cost would be $166, which is more than $ , 0 0 0, Puzzle Time BY THE TIME THEY GET THEIR SHOES ON THE GAME HAS ENDED 5.6 Start Thinking yes; y 5; no Warm Up 1. yes. yes. no 4. yes 5. no 6. no 5.6 Cumulative Review Warm Up 1. y. 6 a 1 7z Copyright Big Ideas Learning, LLC Algebra 1 A57

8 The wrong side was shaded y 0. y Practice B 1. yes. no. no 4. yes 5. yes; You earned 66 points y 1 1. y Sample answer: y y 7. A58 Algebra 1 Copyright Big Ideas Learning, LLC

9 16. y Start Thinking 5.6 Enrichment and Etension 1. and 1; minimum: at, 0, maimum: 1 at 4,. 8 and 4; minimum: 8 at 0, 4, maimum: 4 at 4, 0. 7 and 1; minimum: 7 1 at, and 18; minimum: 5 6, 0 at at 5. a. Sample answer: f, y y b. Sample answer: 6, 7, maimum: 0,1, maimum: 18 at f, y y c. Sample answer: f, y y d. Sample answer: e. Sample answer: f, y 5.6 Puzzle Time A SIT CALM f, y 5y points that are solutions to the system; points that are solutions to one inequality but not the other; yes; the points that are not solutions to either inequality; Sample answer: If the point 0, 0 is plugged into both inequalities, both are true, so the point is a solution to the system; If the point 0, 0 is plugged into both inequalities, neither is true, so the point is not a solution to either inequality in the system. 5.7 Warm Up 1... Copyright Big Ideas Learning, LLC Algebra 1 A59

10 Cumulative Review Warm Up 1. y 4. q 4. p g z Practice A 1. no. yes. yes 4. no 5. no 6. yes , 14. y, 1 A60 Algebra 1 Copyright Big Ideas Learning, LLC

11 15. a. y 60, y b. 8,14 ; This solution represents that 8 bags of red beads and 14 bags of blue beads cost $58, which is less than $60. c. yes 5.7 Practice B 1. yes. no y, y 4 1 y 1, y 11. The incorrect side of the line y was shaded. y 1 y a. Sample answer: 1, y, and y 4 4 b. 8 square units Copyright Big Ideas Learning, LLC Algebra 1 A61

12 5.7 Enrichment and Etension 1. a. y 4, y 0, 0,.5 y 49 b t , 0, 0, 4, 0, 4, 4, 0 c. The combinations are represented by points within the region enclosed by the boundary lines; These are the points that satisfy all four inequalities, and represent all possible combinations of snacks and drinks. d. no; Only whole number points are possible, because you cannot buy fractional drinks or snacks. e. Sample answer: possible: 10 snacks and drinks, not possible: 10 snacks and 5 drinks; The point 10, is inside the shaded region. The point 10, 5 is outside the shaded region. f. Verify response from part (e) by substituting both points into each inequality from part (a). 5.7 Puzzle Time HARE CARE Cumulative Review no solution 1. or a b in in. 15. not a function; The input has two outputs, and not a function; Sample answer: The input 5 has two outputs, 1 and a. y is the dependent variable, and is the independent variable. 18. b. domain: 0 0, range: 5 y a. 8 h b. 5 h 5. 9, no solution 7. z 5, z 1 A6 Algebra 1 Copyright Big Ideas Learning, LLC

13 0. 5. m, b 0 1. a. $90 b. 8 nights. -intercept :, y-intercept : 1 6. m 0, b 6. -intercept : 4, y-intercept : 4 7. m 4, b intercept : 10, y-intercept : 8. The graph of t is a vertical stretch by a factor of followed by a vertical translation 5 units up of the graph of f; domain: all real numbers, range: y 5 9. The graph of r is horizontal translation 1 unit right of the graph of f; domain: all real numbers, range: y 0 0. The graph of h is a vertical shrink by a factor of 1, followed by a reflection in the -ais and a horizontal translation 1 unit right of the graph of f; domain: all real numbers, range: y y y 7. y y 1 Copyright Big Ideas Learning, LLC Algebra 1 A6

14 5. 5 y 4 6. y 1 or y 4 7. y 9 8 or y y 7 or y y or y y y 7 4. y 6 4. no correlation negative correlation 45. not arithmetic 46. arithmetic, arithmetic, 6 54., , ,1 57. three $5 bags and four $ bags 58. 6, , , students per van and students per bus 6. infinitely many solutions; same slope and same y-intercept 6. no solution; same slope but different y-intercepts 64. one solution; different slopes , , domain: all real number, range: y domain: 1, range: y or y 50., 51. 0, 4 5., 5. a. truck driver A: y 7 50, truck driver B: y 175 5, 5 ; From 0 5 miles truck driver b. A is cheaper, at 5 miles both truck drivers charge the same amount, and after 5 miles truck driver B is cheaper. 7. no; It would weigh 100 pounds, which is 00 pounds over the weight limit of the truck. A64 Algebra 1 Copyright Big Ideas Learning, LLC

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