Download solutions

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