Title: Chapter 7 Systems of Equations and Inequalities
Course: quiz duplicate error

Q: What is the solution of the system of equations?
y = –x + 7
y = –2x – 10
- (–17, 24)
- (24, –17)
- (–3, –4)
- (–5.67, 12.67)
A: (–17, 24)

Q: Solve the following system of equations by graphing.
–4x + 3y = –12
–2x + 3y = –18
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.

y = 2x – 3
y = –x + 3
- one solution
- no solutions
- infinitely many solutions
A: one solution

Q: Which graph represents the following system of equations?
y = 3x + 3
y = –x – 3
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.

y = x + 3
y – 3 = x
- infinitely many solutions
- no solutions
- one solution
A: infinitely many solutions

Q: Find a solution to the following system of equations.
[Image]
[Image]
- (–8, –15)
- (–2, –15)
- (0, 1)
- (2, 5)
A: (2, 5)

Q: What is the solution of the system of equations?
y = 3x + 7
y = x – 9
- (–1, –10)
- (–17, –8)
- (4, 19)
- (–8, –17)
A: (–8, –17)

Q: Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding CD a month to his collection while Nita is adding 5 CDs a month to her collection. Write and graph a system to find the number of months after which they will have the same number of CDs. Let x represent the number of months and y the number of CDs.
- [Image] [Image] [Image] 3 months
- [Image] [Image] [Image] 2 months
- [Image] [Image] [Image] 1 month
- [Image] [Image] [Image] 33 months
A: [Image] [Image] [Image] 3 months

Q: Use a graphing calculator to find the solution of the system.
y = [Image]x + [Image]
y = [Image]x + [Image]
- (0, 0.17)
- (5, 6)
- (–5, –4)
- (–1.5, 0)
A: (–5, –4)

Q: Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.

y = –x – 5
y = –x + 3
- no solutions
- one solution
- infinitely many solutions
A: no solutions

Q: What is the solution of the system of equations?
y = –x + 2
y = –3x – 8
- (–2.5, 4.5)
- (–5, 7)
- (–3, 1)
- (7, –5)
A: (–5, 7)

Q: Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.

y = 5x – 4
y = 5x – 5
- no solutions
- one solution
- infinitely many solutions
A: no solutions

Q: Kendra owns a restaurant. She charges $1.50 for 2 eggs and one piece of toast, and $.90 for one egg and one piece of toast. Write and graph a system of equations to determine how much she charges for each egg and each piece of toast. Let x represent the number of eggs and y the number of pieces of toast.
- [Image] [Image] [Image] $.60 per egg, $.30 for toast
- [Image] [Image] [Image] $.30 per egg, $.60 for toast
- [Image] [Image] [Image] $.30 per egg, $.60 for toast
- [Image] [Image] [Image] $.60 per egg, $.30 for toast
A: [Image] [Image] [Image] $.60 per egg, $.30 for toast

Q: Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.

y = 2x – 2
y = –5x – 4
- one solution
- no solutions
- infinitely many solutions
A: one solution

Q: Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.

y = –4x + 4
y = 4x – 2
- one solution
- no solutions
- infinitely many solutions
A: one solution

Q: Find the value of b that makes the system of equations have the solution (3, 5).
y = 3x – 4
y = bx + 2
- 0
- –1
- 2
- 1
A: 1

Q: Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.

y = –x + 4
y – 4 = –x
- infinitely many solutions
- no solutions
- one solution
A: infinitely many solutions

Q: Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.

y = x + 4
y – 4 = x
- infinitely many solutions
- no solutions
- one solution
A: infinitely many solutions

Q: Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.

y = –3x – 4
y = –3x + 2
- no solutions
- one solution
- infinitely many solutions
A: no solutions

Q: Solve the system of equations using substitution.

y = x + 9
y = 2x
- (3, 6)
- (–9, –18)
- (–18, –9)
- (9, 18)
A: (9, 18)

Q: Solve the system of equations using substitution.

y = 2x + 6
y = 5x
- (0.9, 4.3)
- (–2, –10)
- (–10, –2)
- (2, 10)
A: (2, 10)

Q: Solve the system of equations using substitution.

y = 3x + 10
y = 4x + 4
- (–6, –8)
- (–6, –20)
- (6, 28)
- (–8, –6)
A: (6, 28)

Q: Solve the system of equations using substitution.

y = 2x + 3
y = 3x + 1
- (–2, –1)
- (–1, –2)
- (2, 7)
- (–2, –5)
A: (2, 7)

Q: Use substitution to solve the following system of equations.
d + e – f = –3
e = f + d + 3
f =2e – 4
- d = 4, e = 4, f = –3
- d = 3, e = –2, f = 4
- d = –3, e = 4, f = 4
- d = –2, e = 3, f = 4
A: d = –3, e = 4, f = 4

Q: The sum of two numbers is 70. Their difference is 30. Write a system of equations that describes this situation. Solve by elimination to find the two numbers.
- x + y = 30 y – x = 70 45 and 21
- x + y = 70 x – y = 30 50 and 20
- x – y = 70 x + y = 30 49 and 21
- x + y = 70 x – y = 30 45 and 15
A: x + y = 70 x – y = 30 50 and 20

Q: Solve the system of equations using substitution.

y = 3x + 9
y = 4x + 3
- (–6, –9)
- (–6, –21)
- (–9, –6)
- (6, 27)
A: (6, 27)

Q: The length of a rectangle is 2 cm more than four times the width. If the perimeter of the rectangle is 84 cm, what are its dimensions?
- length = 8 cm; width = 34 cm
- length = 34 cm; width = 8 cm
- length = 30 cm; width = 10 cm
- length = 34 cm; width = 10 cm
A: length = 34 cm; width = 8 cm

Q: Solve the system of equations using substitution.

y = 2x – 10
y = 4x – 8
- (3, 4)
- (–1, –12)
- (–4, –17)
- (3, –4)
A: (–1, –12)

Q: The sum of two numbers is 82. Their difference is 26. Write a system of equations that describes this situation. Solve by elimination to find the two numbers.
- x + y = 26 y – x = 82 49 and 29
- x – y = 82 x + y = 26 53 and 29
- x + y = 82 x – y = 26 54 and 28
- x + y = 82 x – y = 26 49 and 23
A: x + y = 82 x – y = 26 54 and 28

Q: Solve the system of equations using substitution.

3x + 2y = 7
y = –3x + 11
- (6, –3)
- (6, –7)
- [Image]
- (5, –4)
A: (5, –4)

Q: The sum of two numbers is 73. Their difference is 27. Write a system of equations that describes this situation. Solve by elimination to find the two numbers.
- x + y = 73 x – y = 27 50 and 23
- x – y = 73 x + y = 27 49 and 24
- x + y = 73 x – y = 27 45 and 18
- x + y = 27 y – x = 73 45 and 24
A: x + y = 73 x – y = 27 50 and 23

Q: Solve the system of equations using substitution.

3y = – [Image]x + 2
y = –x + 9
- (3, 6)
- (20, –4)
- (10, –1)
- (–1, 8)
A: (10, –1)

Q: Solve the system of equations using substitution.

y = x + 6
y = –2x – 3
- (1, 7)
- (–3, 3)
- [Image]
- (4, –11)
A: (–3, 3)

Q: The sum of two numbers is 62. Their difference is 22. Write a system of equations that describes this situation. Solve by elimination to find the two numbers.
- x – y = 62 x + y = 22 41 and 21
- x + y = 62 x – y = 22 42 and 20
- x + y = 62 x – y = 22 37 and 15
- x + y = 22 y – x = 62 37 and 21
A: x + y = 62 x – y = 22 42 and 20

Q: Solve the system of equations using substitution.

y = 4x + 6
y = 2x
- (–3, –6)
- (3, 6)
- (6, 3)
- (1, 2)
A: (–3, –6)

Q: Sharon has some one-dollar bills and some five-dollar bills. She has 14 bills. The value of the bills is $30. Solve a system of equations using elimination to find how many of each kind of bill she has.
- 4 five-dollar bills, 10 one-dollar bills
- 3 five-dollar bills, 10 one-dollar bills
- 5 five-dollar bills, 5 one-dollar bills
- 5 five-dollar bills, 9 one-dollar bills
A: 4 five-dollar bills, 10 one-dollar bills

Q: Solve the system of equations using substitution.

y = 3x – 2
y = 2x – 3
- (–1, –5)
- (1, –1)
- (5, 14)
- (1, 1)
A: (–1, –5)

Q: The sum of two numbers is 82. Their difference is 24. Write a system of equations that describes this situation. Solve by elimination to find the two numbers.
- x + y = 82 x – y = 24 48 and 24
- x – y = 82 x + y = 24 52 and 30
- x + y = 24 y – x = 82 48 and 30
- x + y = 82 x – y = 24 53 and 29
A: x + y = 82 x – y = 24 53 and 29

Q: Solve the system of equations using substitution.

y = 2x + 8
y = 4x
- (–4, –16)
- (4, 16)
- (–16, –4)
- (1.3, 5.3)
A: (4, 16)

Q: The sum of two numbers is 78. Their difference is 18. Write a system of equations that describes this situation. Solve by elimination to find the two numbers.
- x + y = 78 x – y = 18 43 and 25
- x + y = 18 y – x = 78 43 and 31
- x – y = 78 x + y = 18 47 and 31
- x + y = 78 x – y = 18 48 and 30
A: x + y = 78 x – y = 18 48 and 30

Q: The length of a rectangle is 7 cm more than four times the width. If the perimeter of the rectangle is 84 cm, what are its dimensions?
- length = 35 cm; width = 7 cm
- length = 7 cm; width = 35 cm
- length = 35 cm; width = 14 cm
- length = 21 cm; width = 14 cm
A: length = 35 cm; width = 7 cm

Q: The length of a rectangle is 4 cm more than four times the width. If the perimeter of the rectangle is 88 cm, what are its dimensions?
- length = 28 cm; width = 12 cm
- length = 36 cm; width = 12 cm
- length = 36 cm; width = 8 cm
- length = 8 cm; width = 36 cm
A: length = 36 cm; width = 8 cm

Q: Solve the system of equations using substitution.

y = 4x + 10
y = 3x + 5
- (–5, –10)
- (5, 30)
- (30, 5)
- (5, 20)
A: (–5, –10)

Q: Solve the system of equations using substitution.

y = 4x + 4
y = 3x
- (12, 4)
- (4, 12)
- (0.6, 1.7)
- (–4, –12)
A: (–4, –12)

Q: Solve the system of equations using substitution.

y = 2x + 4
y = 3x + 3
- (1, 6)
- (–1, 0)
- (2, –1)
- (–1, 2)
A: (1, 6)

Q: Solve the system of equations using substitution.

y = 2x – 2
y = 4x – 10
- (4, 6)
- (5, 9)
- (2, 2)
- (2, –2)
A: (4, 6)

Q: Use substitution to solve the following system of equations.
d + e – f = 1
e = f + d + 9
f =2e – 6
- d = –3, e = 0, f = –4
- d = –4, e = 1, f = –4
- d = 0, e = –3, f = –4
- d = –4, e = 1, f = –4
A: d = –4, e = 1, f = –4

Q: The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46 centimeters, find the dimensions of the rectangle.
- length = 5 cm; width = 18 cm
- length = 13 cm; width = 5 cm
- length = 13 cm; width = 8 cm
- length = 18 cm; width = 5 cm
A: length = 5 cm; width = 18 cm

Q: Solve the system using elimination.

6x + 3y = –12
6x + 2y = –4
- (10, –16)
- (2, –8)
- (–2, 8)
- (–10, 16)
A: (2, –8)

Q: Solve the system using elimination.

2x – 2y = –8
x + 2y = –1
- (–14, 1)
- (1, 5)
- (–3, 1)
- (0, 4)
A: (–3, 1)

Q: Use substitution to solve the following system of equations.
d + e – f = 11
e = f + d + 5
f =2e – 12
- d = 3, e = 4, f = –4
- d = 3, e = 4, f = –4
- d = 4, e = 3, f = –4
- d = –4, e = 4, f = 3
A: d = 3, e = 4, f = –4

Q: Solve the system using elimination.

10x + 4y = 8
–4x – 6y = 10
- (4, –8)
- (–4, 10)
- (–3, 2)
- (2, –3)
A: (2, –3)

Q: Solve the system using elimination.

–10x – 3y = –24
6x – 4y = 26
- (3, –2)
- (1, 5)
- (6, –10)
- (–2, 3)
A: (3, –2)

Q: Solve the system using elimination.

5x = –25 + 5y
10y = 42 + 2x
- (–1, 2)
- (–1, 4)
- (4, –1)
- (5, 10)
A: (–1, 4)

Q: Solve the system using elimination.

2x + 5y = 8
4x + 15y = 26
- (2, –1)
- (4, 2)
- (–1, 3)
- (–1, 2)
A: (–1, 2)

Q: Solve the system using elimination.

x + 2y = –6
3x + 8y = –20
- (–1, –4)
- (–4, 4)
- (–4, –1)
- (3, 1)
A: (–4, –1)

Q: Solve the system using elimination.

4x + 2y = 14
5x + 8y = 34
- (2, 4)
- (3, 2)
- (5, 4)
- (2, 3)
A: (2, 3)

Q: Solve the system using elimination.

–10x – 3y = –18
–7x – 8y = 11
- (–7, –10)
- (–4, 3)
- (3, –4)
- (2, –1)
A: (3, –4)

Q: Solve the system using elimination.

x + 2y = –5
x – 2y = 15
- (2, 1)
- (6, –5.5)
- (5, –5)
- (–5, 5)
A: (5, –5)

Q: Solve the system using elimination.

5x + 3y = 8
x – 3y = 16
- (4, –4)
- (3, 1)
- (–4, 4)
- (5, –5.7)
A: (4, –4)

Q: Solve the system using elimination.

3x – y = 28
3x + y = 14
- (8, –4)
- (–7, 7)
- (7, –7)
- (–4, 8)
A: (7, –7)

Q: Solve the system using elimination.

5x = 34 + 3y
12y = –46 + 2x
- (–3, 5)
- (5, –3)
- (5, 4)
- (5, 12)
A: (5, –3)

Q: Solve the system using elimination.

5x + 4y = –13
2x – 4y = –22
- (3, –5)
- (–4, 1.8)
- (4, 2)
- (–5, 3)
A: (–5, 3)

Q: Solve the system using elimination.

3x = 9 + 3y
9y = 8 + 2x
- (3, 9)
- (5, 3)
- (2, 5)
- (5, 2)
A: (5, 2)

Q: Solve the system using elimination.

7x – 2y = –39
5x + 7y = –11
- (5, 7)
- (–8, –9)
- (–5, 2)
- (2, –5)
A: (–5, 2)

Q: Solve the system using elimination.

5x + 4y = –29
2x – 4y = –6
- (–5, –1)
- (4, 2)
- (–1, –5)
- (–4, –2.3)
A: (–5, –1)

Q: Solve the system using elimination.

3x + 3y = –9
3x – 3y = 21
- (3, –6)
- (–5, 2)
- (3, 3)
- (2, –5)
A: (2, –5)

Q: Solve the system using elimination.

x + 5y = –9
2x – 5y = 12
- (1, –2)
- (2, –2.2)
- (–2, 1)
- (5, 2)
A: (1, –2)

Q: Solve the system using elimination.

–7x – 8y = –12
9x + 9y = 9
- (5, –4)
- (–4, 5)
- (–7, 8)
- (9, –7)
A: (–4, 5)

Q: A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. Solve by elimination to find the amount of nickels and dimes that are in the jar.
- 30 nickels and 28 dimes
- 31 nickels and 29 dimes
- 29 nickels and 31 dimes
- 30 nickels and 32 dimes
A: 31 nickels and 29 dimes

Q: Solve the system using elimination.

–6x + 5y = 2
9x – 2y = 19
- (3, 4)
- (4, 3)
- (9, –6)
- (5, 6)
A: (3, 4)

Q: Solve the system using elimination.

4x + 3y = –8
5x – 3y = 17
- (2, –5.3)
- (–4, 1)
- (1, –4)
- (3, 5)
A: (1, –4)

Q: Solve the system using elimination.

4x + 4y = –4
x + 8y = –29
- (3, 2)
- (3, –4)
- (1, 4)
- (–4, 3)
A: (3, –4)

Q: Solve the system using elimination.

x + y = 1
3x – y = 7
- (2, –1)
- (–1, 2)
- (3, –2)
- (1, 3)
A: (2, –1)

Q: Solve the system using elimination.

3x + 4y = –25
4x + 12y = –60
- (–3, –4)
- (–3, 3)
- (4, 3)
- (–4, –3)
A: (–3, –4)

Q: Solve the system using elimination.

10x – 7y = 37
–9x – 5y = –22
- (–1, 3)
- (6, 3)
- (3, –1)
- (–9, 10)
A: (3, –1)

Q: Solve the system using elimination.

2x + 4y = 8
5x – 4y = –22
- (4, 5)
- (3, –2)
- (–1, 2.5)
- (–2, 3)
A: (–2, 3)

Q: Solve the system using elimination.

2x + 4y = –16
2x + 12y = –32
- (–2, –4)
- (–4, 3)
- (–4, –2)
- (2, 2)
A: (–4, –2)

Q: Solve the system using elimination.

3x – 4y = 9
–3x + 2y = 9
- (3, 9)
- (–27, –9)
- (–3, –6)
- (–9, –9)
A: (–9, –9)

Q: Solve the system using elimination.

4x + 4y = 0
5x + 12y = –14
- (2, –2)
- (5, 4)
- (2, 3)
- (–2, 2)
A: (2, –2)

Q: Solve the system using elimination.

5x = –20 + 5y
20y = 46 + 3x
- (–2, 4)
- (5, 20)
- (–2, 2)
- (2, –2)
A: (–2, 2)

Q: Solve the system using elimination.

2x = –24 + 4y
16y = 90 + 5x
- (–2, 4)
- (–2, 5)
- (5, –2)
- (2, 16)
A: (–2, 5)

Q: Solve the system using elimination.

5x + 8y = –29
7x – 2y = –67
- (–7, 9)
- [Image]
- (–1, –3)
- (–9, 2)
A: (–9, 2)

Q: Solve the system using elimination.

3x – 4y = –24
x + y = –1
- (–4, 3)
- (0, 6)
- (3, 4)
- (4, 3)
A: (–4, 3)

Q: Graph the inequality.

[Image]
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Write the following inequality in slope-intercept form.
[Image]
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: By what number should you multiply the first equation to solve using elimination?
–5x – 5y = 15
–15x + 4y = 26
- –5
- –15
- 3
- 4
A: 3

Q: Mrs. Huang operates a soybean farm. She buys many supplies in bulk. Often the bulk products need to be custom mixed before Mrs. Huang can use them. To apply herbicide to a large field she must mix a solution of 67% herbicide with a solution of 46% herbicide to form 42 liters of a 55% solution. How much of the 67% solution must she use?
- 23 L
- 18 L
- 34 L
- 35 L
A: 18 L

Q: At the local ballpark, the team charges $6 for each ticket and expects to make $1,200 in concessions. The team must pay its players $1,200 and pay all other workers $1,800. Each fan gets a free bat that costs the team $2 per bat. How many tickets must be sold to break even?
- 300
- 225
- 450
- 1,050
A: 450

Q: At the local ballpark, the team charges $5 for each ticket and expects to make $1,400 in concessions. The team must pay its players $2,000 and pay all other workers $1,600. Each fan gets a free bat that costs the team $3 per bat. How many tickets must be sold to break even?
- 440
- 1,100
- 2,500
- 275
A: 1,100

Q: By what number should you multiply the first equation to solve using elimination?
–3x – 2y = 2
–9x + 3y = 24
- 6
- –9
- –3
- 3
A: 3

Q: At the local ballpark, the team charges $4 for each ticket and expects to make $1,300 in concessions. The team must pay its players $1,500 and pay all other workers $1,600. Each fan gets a free bat that costs the team $2 per bat. How many tickets must be sold to break even?
- 2,200
- 300
- 900
- 450
A: 900

Q: A motorboat can go 8 miles downstream on a river in 20 minutes. It takes 30 minutes for the boat to go upstream the same 8 miles. Find the speed of the current.
- 20 mph
- 16 mph
- 24 mph
- 4 mph
A: 4 mph

Q: By what number should you multiply the first equation to solve using elimination?
3x – 2y = –8
6x + 5y = –7
- 6
- 1
- 3
- 2
A: 2

Q: By what number should you multiply the first equation to solve using elimination?
5x – 4y = 6
15x + y = 31
- 4
- 15
- 3
- 5
A: 3

Q: An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged $32.00. Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates. She was charged $35.25. What is the admission fee? What is the rental fee for a pair of skates?
- admission fee: $3.25 skate rental fee: $2.50
- admission fee: $3.50 skate rental fee: $3.00
- admission fee: $3.00 skate rental fee: $2.00
- admission fee: $4.00 skate rental fee: $3.50
A: admission fee: $3.25 skate rental fee: $2.50

Q: Mike and Kim invest $12,000 in equipment to print yearbooks for schools. Each yearbook costs $4 to print and sells for $16. How many yearbooks must they sell before their business breaks even?
- 3,000
- 1,500
- 750
- 1,000
A: 1,000

Q: You decide to market your own custom computer software. You must invest $3,255 for computer hardware, and spend $2.90 to buy and package each disk. If each program sells for $13.75, how many copies must you sell to break even?
- 196 copies
- 301 copies
- 300 copies
- 195 copies
A: 300 copies

Q: Mike and Kim invest $14,000 in equipment to print yearbooks for schools. Each yearbook costs $7 to print and sells for $35. How many yearbooks must they sell before their business breaks even?
- 650
- 2,000
- 500
- 400
A: 500

Q: You have $31 to spend at the music store. Each cassette tape costs $7 and each CD costs $13. Write and graph a linear inequality that represents this situation. Let x represent the number of tapes and y the number of CDs.
- [Image] [Image]
- [Image] [Image]
- [Image] [Image]
- [Image] [Image]
A: [Image] [Image]

Q: Write the linear inequality shown in the graph.

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A: [Image]

Q: An electronics store makes a profit of $72 for every standard CD player sold and $90 for every portable CD player sold. The manager’s target is to make at least $360 a day on sales from standard and portable CD players.

a. | Write an inequality that represents the numbers of both kinds of CD players that can be sold to reach or exceed the sales target. Let s represent the number of standard CD players and p represent the number of portable CD players.
b. | Write three possible solutions to the problem.
c. | Graph the inequality.
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A: [Image] [Image]

Q: You have $47 to spend at the music store. Each cassette tape costs $5 and each CD costs $10. Write and graph a linear inequality that represents this situation. Let x represent the number of tapes and y the number of CDs.
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A: [Image] [Image]

Q: A doctor’s office schedules 10-minute and 20-minute appointments. The doctor also makes hospital rounds for four hours each weekday.

a. | Suppose the doctor limits these activities to, at most, 30 hours per week. Write an inequality to represent the number of each type of office visit she may have in a week. Let x represent the number of 10-minute appointments and y the number of 20-minute appointments.
b. | Graph the inequality.
c. | Is (63, 30) a solution of the inequality?
- [Image] [Image] yes
- [Image] [Image] no
- [Image] [Image] no
- [Image] [Image] yes
A: [Image] [Image] no

Q: Find a solution of the linear inequality.
[Image]
- (3, 4)
- (2, 1)
- (3, 0)
- (1, 1)
A: (1, 1)

Q: Find a solution of the system of linear inequalities.

[Image]
[Image]
- (1, 2)
- (0, –1)
- (2, 17)
- (–2, –5)
A: (2, 17)

Ronald is setting up an aquarium in his new office. At one pet store, fish cost $2 each and an aquarium cost $40. At another pet store, fish cost $3 each and an aquarium cost $36. Write and solve a system of equations to represent the cost of x fish and an aquarium at each store. Solve this the system. What does this solution represent? If Ronald wants 5 fish, from which pet store should he buy his aquarium? Explain.

Q: Write a system of inequalities for the graph.

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A: [Image] [Image]

Describe how to determine when elimination should be used to solve a system of equations, and how to determine whether to use addition, subtraction, or multiplication.

Tim has $12 to spend at the produce market. He wants to buy some tomatoes at $3 per pound, and some apples at $2 per pound. Tim writes the following linear inequality to determine how many pounds of each item he can buy; [Image]. Explain what values of x and y are reasonable.

Graph the following equation.

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A local citizen wants to fence a rectangular community garden. The length of the garden should be at least 110 ft, and the distance around should be no more than 380 ft.

a. | Write a system of inequalities that models the possible dimensions of the garden.
b. | Graph the system to show all possible solutions.

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A motorboat can go 16 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go back upstream the same 16 miles.
Let x = the speed of the boat.
Let y = the speed of the current.

a. | Write an equation for the motion of the motorboat downstream.
b. | Write an equation for the motion of the motorboat upstream.
c. | Find the speed of the current.

Amy’s restaurant has budgeted at most $60 to spend this month on gourmet coffee. All international blends cost $8.50 per package and all house blends cost $6.00 per package. She would like to purchase some international blends and at least 3 packages of the house blends. How can Amy spend $60 on x international blends and y house blends?

a. | Write a system of linear inequalities that describes this situation.
b. | Graph the system.
c. | Give a possible solution and describe what it means.

Without solving, what method would you choose to solve the system: graphing, substitution, or elimination? Explain your reasoning.

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[Image]

Niki has 8 coins worth $1.40. Some of the coins are nickels and some are quarters.

a. | Let q = the number of quarters and n = the number of nickels. Write an equation relating the number of quarters and nickels to the total number of coins.
b. | Write an equation relating the value of the quarters and the value of the nickels to the total value of the coins.
c. | How many of each coin does Niki have?

Write the inequality y is less than x plus 4. Explain how to graph the inequality. Then graph the inequality.

Q: Solve the system of linear inequalities by graphing.

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[Image]
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A: [Image]

Tickets to a local movie were sold at $6.00 for adults and $4.50 for students. There were 240 tickets sold for a total of $1,155.00.

a. | Write a system of equations to model the situation.
b. | Solve the system to find the number of adult tickets sold and the number of student tickets sold.
c. | Explain the method you used to solve the system.

Without graphing, decide whether the system has one solution, no solution, or infinitelymanysolutions. Explain.

[Image]
[Image]

Graph the following linear inequalities on the same coordinate plane. What figure does the solution to all three inequalities make?

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[Image]
[Image]

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You have a gift certificate to a book store worth $90. Each paperback books is $9 and each hardcover books is $12. You must spend at least $25 in order to use the gift certificate. Write and graph a system of inequalities to model the number of each kind of books you can buy. Let x = the number of paperback books and y = the number of hardback books.

[Image]

Q: Find a solution of the system of linear inequalities.

[Image]
[Image]
- (4, 1)
- (2, 2)
- (1, 2)
- (5, 2)
A: (5, 2)