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The slope is 1 and the y-intercept is –8. Chapter Review State the slope and the y-intercept of the graph of each equation. 17. y = 4x + 7 SOLUTION: y = 4x + 7 The slope is 4 and the y-intercept is 7. ANSWER: 4; 7 18. y = ANSWER: 1; –8 21. y = –8x – 7 SOLUTION: y = –8x – 7 The slope is –8 and the y-intercept is –7. ANSWER: –8; –7 22. 4x – y = 6 SOLUTION: First solve for y. x SOLUTION: y=– x+0 The slope is – and the y-intercept is 0. ANSWER: The slope is 4 and the y-intercept is –6. – ANSWER: 4; –6 ;0 19. 5x + y = 0 SOLUTION: First solve for y. The slope is –5 and the y-intercept is 0. ANSWER: –5; 0 20. –x + y = –8 Graph each equation using the slope and yintercept. 23. y = –x + 4 SOLUTION: y = –x + 4 slope = –1 y-intercept = 4 Graph the y-intercept point at (0, 4), then use the slope to locate a second point on the line. Another point on the line is (–1, 5). SOLUTION: First solve for y. The slope is 1 and the y-intercept is –8. ANSWER: 1; –8 21. y = –8x – 7 SOLUTION: y = –8x – 7- Powered by Cognero eSolutions Manual The slope is –8 and the y-intercept is –7. ANSWER: ANSWER: Page 1 The slope is 4 and the y-intercept is –6. ANSWER: Chapter Review 4; –6 Graph each equation using the slope and yintercept. 23. y = –x + 4 SOLUTION: y = –x + 4 slope = –1 y-intercept = 4 Graph the y-intercept point at (0, 4), then use the slope to locate a second point on the line. 24. y = 2x – 6 SOLUTION: y = 2x – 6 slope = 2 y-intercept = –6 Graph the y-intercept point at (0, –6), then use the slope to locate a second point on the line. Another point on the line is (1, –4). Another point on the line is (–1, 5). ANSWER: ANSWER: 25. y = 24. y = 2x – 6 SOLUTION: y = 2x – 6 slope = 2 y-intercept = –6 Graph the y-intercept point at (0, –6), then use the slope to locate a second point on the line. x–3 SOLUTION: y= x–3 slope = y-intercept = –3 Graph the y-intercept point at (0, –3), then use the slope to locate a second point on the line. Another point on the line is (1, –4). eSolutions Manual - Powered by Cognero Another point on the line is (2, 0). Page 2 Chapter Review 25. y = x–3 SOLUTION: y= x–3 26. y = x+5 SOLUTION: y= x+5 slope = slope = y-intercept = –3 Graph the y-intercept point at (0, –3), then use the slope to locate a second point on the line. y-intercept = 5 Graph the y-intercept point at (0, 5), then use the slope to locate a second point on the line. Another point on the line is (2, 0). Another point on the line is (4, 4). ANSWER: ANSWER: 26. y = x+5 SOLUTION: y= x+5 slope = y-intercept = 5 Graph the y-intercept point at (0, 5), then use the eSolutions - Powered by Cognero slopeManual to locate a second point on the line. 27. A balloon is rising above the ground. The height in feet y of the balloon can be given by y = 7 + 2x, where x represents the time in seconds. State the slope and y-intercept of the graph of the equation. Describe what they represent. SOLUTION: The slope is 2 and the y-intercept is 7. The slope 2 represents the ascent in ft per second. The y– intercept 7 represents the initial altitude in ft before the balloon is released. Page 3 ANSWER: Slope: 2; y-intercept: 7; the slope 2 represents the Chapter Review 27. A balloon is rising above the ground. The height in feet y of the balloon can be given by y = 7 + 2x, where x represents the time in seconds. State the slope and y-intercept of the graph of the equation. Describe what they represent. SOLUTION: The slope is 2 and the y-intercept is 7. The slope 2 represents the ascent in ft per second. The y– intercept 7 represents the initial altitude in ft before the balloon is released. ANSWER: Slope: 9; y-intercept: 5; the slope represents the cost of each DVD ($9); the y-intercept represents the shipping fee ($5). Solve each system of equations by graphing. 29. y = x y= x–1 SOLUTION: ANSWER: Slope: 2; y-intercept: 7; the slope 2 represents the ascent in ft per second. The y-intercept 7 represents the initial altitude in ft before the balloon is released. 28. Jacob is ordering DVDs from a Web site. The site charges a flat rate for shipping, no matter how many DVDs he buys. The total cost y of Jacob’s order is given by y = 9x + 5, where x represents the number of DVDs he buys. State the slope and y-intercept of the equation. Describe what they represent. SOLUTION: The slope is 9 and the y-intercept is 5. The slope represents the cost of each DVD ($9) and the yintercept represents the shipping fee ($5). The solution of the system of equations is (–2, –2). ANSWER: ANSWER: Slope: 9; y-intercept: 5; the slope represents the cost of each DVD ($9); the y-intercept represents the shipping fee ($5). Solve each system of equations by graphing. 29. y = x y= x–1 SOLUTION: 30. y = x + 2 y = 3x SOLUTION: eSolutions Manual - Powered by Cognero The solution of the system of equations is (–2, –2). Page 4 Chapter Review 30. y = x + 2 y = 3x SOLUTION: 31. y = 2x + 1 x + y = –2 SOLUTION: The solution of the system of equations is (–1, –1). ANSWER: (–1, –1) The solution of the system of equations is (1, 3). ANSWER: 32. 5x – 3y = –3 y = –x + 1 SOLUTION: The solution of the system of equations is (0, 1). ANSWER: (0, 1) 31. y = 2x + 1 x + y = –2 SOLUTION: 33. The sum of two numbers is 9, and the difference of the numbers is 1. Write a system of equations to represent this situation. Then solve the system to find the numbers. SOLUTION: Sample answer: Let x = the first number and y = the second number. x +y = 9 x–y =1 Solve the second equation for x. eSolutions Manual - Powered by Cognero The solution of the system of equations is (–1, –1). ANSWER: Page 5 Substitute y + 1 for x in the first equation. y = 4. The solution of the system of equations is (0, 1). ANSWER: (0, 1) Chapter Review 33. The sum of two numbers is 9, and the difference of the numbers is 1. Write a system of equations to represent this situation. Then solve the system to find the numbers. SOLUTION: Sample answer: Let x = the first number and y = the second number. x +y = 9 x–y =1 Solve the second equation for x. ANSWER: Sample answer: x + y = 9, x – y = 1; 5 and 4; x = 5; y=4 34. A café sells strawberry smoothies and vanilla smoothies. On Monday, the café sold twice as many strawberry smoothies as vanilla smoothies. The total number of smoothies sold was 24. Write a system of equations to represent this situation. Then solve the system and explain what the solution means. SOLUTION: Sample answer: Let x = the number of vanilla smoothies and y = the number of strawberry smoothies. y = 2x x + y = 24 Substitute 2x for y in the second equation. Substitute y + 1 for x in the first equation. Now substitute x = 8 into either equation to find y. Now substitute y = 4 into either equation to find x. The solution of this system of equations is x = 5 and y = 4. ANSWER: Sample answer: x + y = 9, x – y = 1; 5 and 4; x = 5; y=4 34. A café sells strawberry smoothies and vanilla smoothies. On Monday, the café sold twice as many strawberry smoothies as vanilla smoothies. The total number of smoothies sold was 24. Write a system of equations to represent this situation. Then solve the system and explain what the solution means. SOLUTION: Sample answer: Let x = the number of vanilla smoothies and y = the number of strawberry smoothies. y = 2x x + y = 24 Substitute 2x for y in the second equation. The solution of this system of equations is x = 8 and y = 16. This means the café sold 8 vanilla smoothies and 16 strawberry smoothies. ANSWER: Sample answer: y = 2x, x + y = 24; x = 8, y = 16; the café sold 8 vanilla smoothies and 16 strawberry smoothies. Solve each system algebraically. 35. y = 4 y = 3x – 11 SOLUTION: Replace y with 4 in the second equation. The solution is (5, 4). ANSWER: (5, 4) 36. y = 6 – x x = –1 eSolutions Manual - Powered by Cognero Now substitute x = 8 into either equation to find y. SOLUTION: Replace x with –1 in the first equation. Page 6 The solution is (5, 4). ANSWER: (5, 4) Chapter Review 36. y = 6 – x x = –1 SOLUTION: Replace x with –1 in the first equation. The solution is (0, 2). ANSWER: (0, 2) 38. –4x + y = 6 –5x – y = 21 SOLUTION: Solve the first equation for y. Replace y with 6 + 4x in the second equation. The solution is (–1, 7). ANSWER: (–1, 7) 37. –5x + y = 2 –3x + 6y = 12 SOLUTION: Solve the first equation for y. Substitute –3 for x in either equation to find the value of y. Replace y with 2 + 5x in the second equation. The solution is (–3, –6). ANSWER: (–3, –6) Substitute 0 for x in either equation to find the value of y. 39. 2x – 4y = 6 3x – 5y = 11 SOLUTION: Solve the first equation for x. The solution is (0, 2). ANSWER: (0, 2) Replace x with 3 + 2y in the second equation. 38. –4x + y = 6 –5x – y = 21 SOLUTION: Solve the first equation for y. eSolutions Manual - Powered by Cognero Replace y with 6 + 4x in the second equation. Page 7 Substitute 2 for y in either equation to find the value of x. The solution is (–3, –6). ANSWER: Chapter Review (–3, –6) 39. 2x – 4y = 6 3x – 5y = 11 SOLUTION: Solve the first equation for x. 8y = 8y is a true statement. This system has infinitely many solutions. ANSWER: infinitely many solutions 41. 7x – 3y = –4 7x = –2 + 3y SOLUTION: Solve the first equation for x. Replace x with 3 + 2y in the second equation. Replace x with in the second equation. Substitute 2 for y in either equation to find the value of x. –4 = –2 is a false statement. This system has no solution. ANSWER: no solution 42. 2x + y = 3 y = –3x + 7 The solution is (7, 2). ANSWER: (7, 2) SOLUTION: Since y = –3x + 7, replace y with –3x + 7 in the first equation. 40. 8y = 6 – 2x x = 3 – 4y SOLUTION: Since, x = 3 – 4y, replace x with 3 – 4y in the first equation. Substitute 4 for x in either equation to find the value of y. 8y = 8y is a true statement. This system has infinitely many solutions. ANSWER: infinitely many solutions 3y = –4 41. 7x –Manual eSolutions - Powered by Cognero 7x = –2 + 3y SOLUTION: The solution is (4, –5). ANSWER: (4, –5) Page 8 43. One number subtracted from three times another –4 = –2 is a false statement. This system has no solution. ANSWER: Chapter Review no solution 42. 2x + y = 3 y = –3x + 7 SOLUTION: Since y = –3x + 7, replace y with –3x + 7 in the first equation. Substitute 4 for x in either equation to find the value of y. The solution is (4, –5). ANSWER: (4, –5) 43. One number subtracted from three times another number is 11. The sum of the numbers is 1. Write and solve a system of equations to represent this situation. Interpret the solution. SOLUTION: Let x = the first number and let y = the second number. 3x – y = 11 x +y =1 Solve the second equation for x. Replace x with 1 – y in the first equation. The solution is (4, –5). ANSWER: (4, –5) 43. One number subtracted from three times another number is 11. The sum of the numbers is 1. Write and solve a system of equations to represent this situation. Interpret the solution. SOLUTION: Let x = the first number and let y = the second number. 3x – y = 11 x +y =1 Solve the second equation for x. Replace x with 1 – y in the first equation. Substitute –2 for y in either equation to find the value of x. The solution is (3, –2). This means one number is 3 and the other number is –2. ANSWER: 3x – y = 11; x + y = 1; (3, –2); One number is 3; the other number is –2. 44. Tickets to a museum cost $3 for children and $8 for adults. A group of four visitors to the museum spent a total of $22 on tickets. Write and solve a system of equations to represent this situation. Interpret the solution. SOLUTION: Let x = the number of children and y = the number of adults. x +y =4 3x + 8y = 22 Solve the first equation for x. Substitute –2 for y in either equation to find the value of x.Manual - Powered by Cognero eSolutions Page 9 Replace x with 4 – y in the second equation. and the other number is –2. ANSWER: 3x – y = 11; x + y = 1; (3, –2); One number is 3; the other number is –2. Chapter Review 44. Tickets to a museum cost $3 for children and $8 for adults. A group of four visitors to the museum spent a total of $22 on tickets. Write and solve a system of equations to represent this situation. Interpret the solution. SOLUTION: Let x = the number of children and y = the number of adults. x +y =4 3x + 8y = 22 Solve the first equation for x. Replace x with 4 – y in the second equation. Substitute 2 for y in either equation. The solution is (2, 2). This means there were two children and two adults in the group. ANSWER: x + y = 4; 3x + 8y = 22; (2, 2); There were two children and two adults in the group. eSolutions Manual - Powered by Cognero Page 10