Deck 8: Systems of Equations and Inequalities

Question 1

Solve Linear Systems by Substitution
$$2 y = x + 24$$
$5 x + 10 y = 0$

A) $\{ ( - 12,6 ) \}$
B) $\{ ( 6 , - 12 ) \}$
C) $\{ ( - 12 , - 6 ) \}$
D) $\{ ( 12,5 ) \}$

Answer 1

A

Question 2

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( - 3,3 ) \\4 x - y = - 9 \\2 x + 4 y = 6\end{array}$$

A) not a solution
B) solution

Answer 2

A

Question 3

Solve Linear Systems by Substitution
$$\begin{array} { c } x + 8 y = - 49 \\- 4 x + 7 y = - 77\end{array}$$

A) $\{ ( 7 , - 7 ) \}$
B) $\{ ( 6 , - 6 ) \}$
C) $\{ ( - 7 , - 6 ) \}$
D) $\varnothing$

Answer 3

A

Question 4

Solve Linear Systems by Substitution
$$\begin{aligned}- 5 x + 2 y & = 72 \\x - 4 y & = 0\end{aligned}$$
$$x - 4 y = 0$$

A) $\{ ( - 16 , - 4 ) \}$
B) $\{ ( - 4 , - 16 ) \}$
C) $\{ ( - 16,4 ) \}$
D) $\{ ( - 15 , - 4 ) \}$

Question 5

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( - 2 , - 4 ) \\3 x + y = - 2 \\4 x + 3 y = 4\end{array}$$

A) not a solution
B) solution

Question 6

Solve Linear Systems by Substitution
$$\begin{array} { l } 9 x + y = - 13 \\- 9 x - 5 y = 17\end{array}$$

A) $\left\{ \left( - \frac { 4 } { 3 } , - 1 \right) \right\}$
B) $\{ ( 1,11 ) \}$
C) $\{ ( - 5 , - 4 ) \}$
D) $\left\{ \left( - \frac { 1 } { 3 } , - 10 \right) \right\}$

Question 7

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( - 1 , - 6 ) \\2 x - y = - 8 \\3 x - 2 y = - 15\end{array}$$

A) not a solution
B) solution

Question 8

Solve Linear Systems by Substitution
$$\begin{aligned}\mathrm { y } & = 3 \mathrm { x } - 1 \\4 \mathrm { y } + 16 \mathrm { x } & = 80\end{aligned}$$

A) $\{ ( 3,8 ) \}$
B) $\{ ( 8,3 ) \}$
C) $\{ ( - 3,8 ) \}$
D) $\varnothing$

Question 9

Solve Linear Systems by Addition
$$\begin{array} { l } x + y = - 8 \\x - y = 19\end{array}$$

A) $\{ ( 5.5 , - 13.5 ) \}$
B) $\{ ( 5.5,13.5 ) \}$
C) $\{ ( 8 , - 13.5 ) \}$
D) $\{ ( 8,5.5 ) \}$

Question 10

Solve Linear Systems by Substitution
$$\begin{array} { l } 3 x - 2 y = - 28 - 3 x \\4 x + 7 y = x + 6 y + - 4\end{array}$$

A) $\{ ( - 3,5 ) \}$
B) $\{ ( - 3 , - 5 ) \}$
C) $\{ ( 0 , - 28 ) \}$
D) $\left\{ \left( - \frac { 14 } { 3 } , 0 \right) \right\}$

Question 11

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( 2 , - 4 ) \\4 x = 4 - y \\2 x = - 12 - 4 y\end{array}$$

A) solution
B) not a solution

Question 12

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( - 5 , - 5 ) \\4 x = 15 - y \\3 x = - 5 - 4 y\end{array}$$

A) not a solution
B) solution

Question 13

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( 1 , - 2 ) \\x + y = - 1 \\x - y = 3\end{array}$$

A) solution
B) not a solution

Question 14

Solve Linear Systems by Substitution
$$\begin{aligned}x + y & = 6 \\y & = - 4 x\end{aligned}$$

A) $\{ ( - 2,8 ) \}$
B) $\{ ( - 2 , - 8 ) \}$
C) $\{ ( 2,8 ) \}$
D) $\{ ( 2 , - 8 ) \}$

Question 15

Solve Linear Systems by Substitution
$$\begin{array} { l } y = 2 x - 6 \\y = 7 x - 5\end{array}$$

A) $\left\{ \left( - \frac { 1 } { 5 } , - \frac { 32 } { 5 } \right) \right\}$
B) $\left\{ \left( - \frac { 32 } { 5 } , - \frac { 1 } { 5 } \right) \right\}$
C) $\{ ( 1 , - 4 ) \}$
D) $\varnothing$

Question 16

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( 3,3 ) \\x + y = 0 \\x - y = - 6\end{array}$$

A) not a solution
B) solution

Question 17

Solve Linear Systems by Substitution
$$\begin{array} { l } y = \frac { 1 } { 6 } x - 7 \\y = \frac { 2 } { 3 } x + 11\end{array}$$

A) $\{ ( - 36 , - 13 ) \}$
B) $\{ ( - 36,13 ) \}$
C) $\{ ( 42,0 ) \}$
D) $\left\{ \left( - \frac { 35 } { 6 } , - \frac { 53 } { 3 } \right) \right\}$

Question 18

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( - 5 , - 6 ) \\2 x + y = - 16 \\4 x + 2 y = - 32\end{array}$$

A) solution
B) not a solution

Question 19

Solve Linear Systems by Substitution
$$\begin{array} { l } 9 x + 8 y = 62 \\7 x - 5 y = 37\end{array}$$

A) $\{ ( 6,1 ) \}$
B) $\{ ( 5,2 ) \}$
C) $\{ ( 6,2 ) \}$
D) $\varnothing$

Question 20

Solve Linear Systems by Substitution
$$\begin{array} { r } 2 x + 5 y = - 9 \\x = 2 y\end{array}$$

A) $\{ ( - 2 , - 1 ) \}$
B) $\{ ( - 1 , - 2 ) \}$
C) $\{ ( - 2,1 ) \}$
D) $\{ ( - 1 , - 1 ) \}$

Question 21

Solve Linear Systems by Addition
$$\begin{array} { l } 6 x + 8 y = 8 \\6 x - 2 y = - 2\end{array}$$

A) $\{ ( 0,1 ) \}$
В) $\{ ( 1,0 ) \}$
C) $\{ ( 1,1 ) \}$
D) $\{ ( 0,0 ) \}$

Question 22

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\begin{array} { l } y = 18 - 5 x \\5 x + y = 28\end{array}$$

A) $\{ ( 12,13 ) \}$
B) $\{ ( 15,3 ) \}$
C) $\{ ( x , y ) \mid 5 x + y = 18 \}$
D) $\varnothing$ )

Question 23

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\begin{array} { l } 4 x + y = 3 \\2 y = 6 - 8 x\end{array}$$

A) $\left\{ \left[ \frac { 3 } { 4 } , 0 \right) \right\}$
B) $\{ ( 0,3 ) \}$
C) $\{ ( x , y ) \mid 4 x + y = 3 \}$
D) $\varnothing$

Question 24

Solve Linear Systems by Addition
$$\begin{array} { l } - 3 x + 7 y = 24 \\- 5 x - 4 y = - 7\end{array}$$

A) $\{ ( - 1,3 ) \}$
В) $\{ ( 1 , - 3 ) \}$
C) $\{ ( - 1 , - 3 ) \}$
D) $\{ ( 1,3 ) \}$

Question 25

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\begin{array} { l } 9 x - 2 y = 7 \\- 27 x + 6 y = - 14\end{array}$$

A) $\{ ( 3,2 ) \}$
B) $\left\{ \left( \frac { 18 } { 7 } , - \frac { 4 } { 7 } \right) \right\}$
C) $\{ ( x , y ) \mid 9 x - 2 y = 7 \}$
D) $\varnothing$

Question 26

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\begin{array} { l } x - 3 y = 5 \\- 6 x - 4 y = 36\end{array}$$

A) $\{ ( - 4 , - 3 ) \}$
В) $\{ ( - 5 , - 2 ) \}$
C) $\{ ( x , y ) \mid x - 3 y = 5 \}$
D) $\varnothing$

Question 27

Solve Linear Systems by Addition
$$\begin{array} { l } 3 x + 7 y = 46 \\3 x + 2 y = 56\end{array}$$

A) $\{ ( 20 , - 2 ) \}$
В) $\{ ( - 20,3 ) \}$
C) $\{ ( - 20,7 ) \}$
D) $\{ ( - 2,20 ) \}$

Question 28

Solve Linear Systems by Addition
$$\begin{array} { l } 2 x + 15 y = - 91 \\9 x + 3 y = 42\end{array}$$

A) $\{ ( 7 , - 7 ) \}$
B) $\{ ( - 7,7 ) \}$
C) $\{ ( 9 , - 9 ) \}$
D) $\{ ( - 3,7 ) \}$

Question 29

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\begin{array} { l } x + y = - 1 \\x - y = 17\end{array}$$

A) $\{ ( 8 , - 9 ) \}$
B) $\{ ( 8,9 ) \}$
C) $\{ ( x , y ) \mid x + y = - 1 \}$
D) $\varnothing$

Question 30

Solve Linear Systems by Addition
$$\begin{array} { l } 8 x + 6 y = 28 \\4 x - 2 y = 24\end{array}$$

A) $\{ ( 5 , - 2 ) \}$
B) $\{ ( 4 , - 1 ) \}$
C) $\{ ( 5 , - 1 ) \}$
D) $\varnothing$

Question 31

Solve Linear Systems by Addition
$$\begin{array} { r } 6 x + 2 y = - 6 \\- 6 x - 9 y = 48\end{array}$$

A) $\{ ( 1 , - 6 ) \}$
B) $\{ ( - 1,6 ) \}$
C) $\{ ( - 1 , - 6 ) \}$
D) $\varnothing$

Question 32

Solve Linear Systems by Addition
$$\begin{array} { l } - 3 x + y = - 2 \\3 x + 4 y = 17\end{array}$$

A) $\left\{ \left( \frac { 5 } { 3 } , 3 \right) \right\}$
В) $\{ ( 1,8 ) \}$
C) $\left\{ \left( 4 , \frac { 5 } { 4 } \right) \right\}$
D) $\left\{ \left( \frac { 8 } { 3 } , 6 \right) \right\}$

Question 33

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\begin{array} { l } x + y = 5 \\x + y = - 4\end{array}$$

A) $\{ ( 0,1 ) \}$
B) $\{ ( 5 , - 4 ) \}$
C) $\{ ( x , y ) \mid x + y = 5 \}$
D) $\varnothing$

Question 34

Solve Linear Systems by Addition
$$\begin{array} { l } 6 y = 63 - 7 x \\2 x = 78 - 6 y\end{array}$$

A) $\{ ( - 3,14 ) \}$
B) $\{ ( 6 , - 14 ) \}$
C) $\{ ( 7 , - 14 ) \}$
D) $\varnothing$

Question 35

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\begin{array} { l } 6 y = 48 - 5 x \\2 x = 66 - 6 y\end{array}$$

A) $\{ ( - 6,13 ) \}$
B) $\{ ( 6 , - 13 ) \}$
C) $\{ ( x , y ) \mid 5 x + 6 y = 48 \}$
D) $\varnothing$

Question 36

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\begin{array} { l } 3 x + y = 11 \\9 x + 3 y = 33\end{array}$$

A) $\{ ( 0,11 ) \}$
B) $\{ ( 5 , - 4 ) \}$
C) $\{ ( x , y ) \mid 3 x + y = 11 \}$
D) $\varnothing$ )

Question 37

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\begin{array} { l } y = - 5 x - 4 \\- 10 x - 2 y = 8\end{array}$$

A) $\{ ( 0 , - 4 ) \}$
B) $\{ ( 0,0 ) \}$
C) $\{ ( x , y ) \mid 5 x + y = - 4 \}$
D) $\varnothing$

Question 38

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\begin{array} { l } x + 6 y = 3 \\5 x + 30 y = 15\end{array}$$

A) $\{ ( 3,0 ) \}$
B) $\{ ( 0,0 ) \}$
C) $\{ ( x , y ) \mid x + 6 y = 3 \}$
D) $\varnothing$

Question 39

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\begin{array} { l } y = 15 - 4 x \\16 x + 4 y = 60\end{array}$$

A) $\{ ( 0,15 ) \}$
B) $\{ ( 5 , - 5 ) \}$
C) $\{ ( x , y ) \mid 4 x + y = 15 \}$
D) $\varnothing$ )

Question 40

Solve Linear Systems by Addition
$$\begin{array} { c } x - 6 y = - 35 \\- 4 x - 7 y = - 15\end{array}$$

A) $\{ ( - 5,5 ) \}$
В) $\{ ( - 6,6 ) \}$
C) $\{ ( 5,6 ) \}$
D) $\varnothing$

Question 41

Solve Problems Using Systems of Linear Equations
Steve invests in a circus production. The cost includes an overhead of $\$ 117,000$ , plus production costs of $\$ 7000$ per performance. A sold-out performance brings in $\$ 16,000$ . Determine the dollar amount coming in and going out at the break-even point.

A) $\$ 208,000$
B) $\$ 91,000$
C) $\$ 13$
D) $\$ 81,391$

Question 42

Solve Problems Using Systems of Linear Equations
One number is 3 less than a second number. Twice the second number is 18 less than 5 times the first. Find the two numbers.

A) 8 and 11
B) 7 and 10
C) 9 and 12
D) $- 11$ and $- 8$

Question 43

Solve Problems Using Systems of Linear Equations
Steve invests in a circus production. The cost includes an overhead of $\$ 16,000$ , plus production costs of $\$ 8000$ per performance. A sold-out performance brings in $\$ 10,000$ . Determine the number of sold-out performances, $x$ , needed to break even.

A) 8 performances
B) 9 performances
C) 10 performances
D) 2 performances

Question 44

Solve Problems Using Systems of Linear Equations
Is there a profit when 910 binoculars are produced?

A) Yes
B) $\mathrm { No }$

Question 45

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\begin{array} { l } \frac { x } { 7 } + \frac { y } { 14 } = 1 \\\frac { x } { 2 } - \frac { y } { 4 } = 0\end{array}$$

A) $\left\{ \left\{ \frac { 7 } { 2 } , 7 \right) \right\}$
B) $\left\{ \left( 7 , \frac { 7 } { 2 } \right\} \right\}$
C) $\left\{ ( x , y ) \mid \frac { x } { 7 } + \frac { y } { 14 } = 1 \right\}$
D) $\varnothing$

Question 46

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\frac { x } { 3 } + \frac { y } { 3 } = 0$$
$x - y = - 8$

A) $\{ ( - 4,4 ) \}$
B) $\{ ( - 5,5 ) \}$
C) $\{ ( x , y ) \mid x - y = - 8 \}$
D) $\varnothing$

Question 47

Solve Problems Using Systems of Linear Equations
How many binoculars must be produced and sold for the company to break even?

A) 750 binoculars
B) 2250 binoculars
C) 1500 binoculars
D) 2700 binoculars

Question 48

Solve Problems Using Systems of Linear Equations
Use the revenue and cost functions to write the profit function from producing and selling $x$ binoculars.

A) $P ( x ) = 2 x - 1500$
B) $P ( x ) = 2 x + 1500$
C) $P ( x ) = 4 x + 1500$
D) $P ( x ) = 4 x - 1500$

Question 49

Solve Problems Using Systems of Linear Equations
An-Mei owns a business making and selling jackets. She has a fixed cost of $\$ 4500$ . It costs $\$ 85$ to produce each jacket. The selling price is $\$ 115$ per jacket. Let $x$ represent the number of jackets produced and sold and write the cost function, $C$ , and revenue function, $R$ .

A) $C ( x ) = 85 x + 4500$
$R ( x ) = 115 x$
B) $C ( x ) = 85 + 115 x$
$R ( x ) = 4500 x$
C) $C ( x ) = 85 + 4500 x$
$R ( x ) = 115$
D) $C ( x ) = 85 x + 4500 x$
$R ( x ) = 115 x$

Question 50

Solve Problems Using Systems of Linear Equations
One number is 8 less than a second number. Twice the second number is 61 more than 5 times the first. Find the two numbers.

A) $- 15$ and $- 7$
B) $- 16$ and $- 8$
C) $- 14$ and $- 6$
D) 7 and 15

Question 51

Solve Problems Using Systems of Linear Equations
What is the profit when 964 binoculars are produced?

A) $\$ 428$
B) $\$ 3428$
C) $\$ 2356$
D) $\$ 5356$

Question 52

Solve Problems Using Systems of Linear Equations
Fewer than how many binoculars must be produced and sold for the company to have a profit loss?

A) 750 binoculars
B) 2250 binoculars
C) 1500 binoculars
D) 2700 binoculars

Question 53

Solve Problems Using Systems of Linear Equations
Two cars leave a city and head in the same direction. After 7 hours, the faster car is 63 miles ahead of the slower car. The slower car has traveled 336 miles. Find the speeds of the two cars.

A) $48 \mathrm { mph }$ and $57 \mathrm { mph }$
B) $50 \mathrm { mph }$ and $59 \mathrm { mph }$
C) $90 \mathrm { mph }$ and $99 \mathrm { mph }$
D) $39 \mathrm { mph }$ and $48 \mathrm { mph }$ The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.
$$\text { Binoculars Produced and Sold }$$

Question 54

Solve Problems Using Systems of Linear Equations
At the break-even point both cost and revenue are what?

A) $\$ 2250$
B) $\$ 750$
C) $\$ 1500$
D) $\$ 2700$

Question 55

Solve Problems Using Systems of Linear Equations
The sum of two numbers is 9 . If one number is subtracted from the other, their difference is $- 1$ . Find the numbers.

A) 4,5
B) $4 , - 5$
C) $- 4,5$
D) 6,3

Question 56

Solve Problems Using Systems of Linear Equations
More than how many binoculars must be produced and sold for the company to have a profit gain?

A) 750 binoculars
B) 2250 binoculars
C) 1500 binoculars
D) 2700 binoculars

Question 57

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$\begin{array} { l } 8 x - 3 y = 3 \\- 16 x + 6 y = - 9\end{array}$$

A) $\left\{ \left( \frac { 4 } { 3 } , - \frac { 1 } { 2 } \right) \right\}$
B) $\{ ( 2,3 ) \}$
C) $\{ ( x , y ) \mid 8 x - 3 y = 3 \}$
D) $\varnothing$

Question 58

Solve Problems Using Systems of Linear Equations
Steve invests in a circus production. The cost includes an overhead of $\$ 36,000$ , plus production costs of $\$ 5000$ per performance. A sold-out performance brings in $\$ 8000$ . Let $x$ represent the number of sold-out performances and write the cost function, $C$ and revenue function, $R$ .

A) $C ( x ) = 36,000 + 5000 x$
$R ( x ) = 8000 x$
B) $C ( x ) = 36,000 + 8000 x$
$R ( x ) = 5000 x$
C) $C ( x ) = 5000 x$
$R ( x ) = 36,000 + 8000 x$
D) $C ( x ) = 36,000 x + 5000$
$R ( x ) = 8000 x$

Question 59

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
$$y = \frac { 1 } { 2 } x + 3$$
$$x - 2 y = - 6$$

A) $\{ ( - 6,0 ) \}$
B) $\{ ( 0,3 ) \}$
C) $\{ ( x , y ) \mid x - 2 y = - 6 \}$
D) $\varnothing$

Question 60

Solve Problems Using Systems of Linear Equations
Is there a profit when 238 binoculars are produced?

A) $\mathrm { No }$
B) Yes

Question 61

Solve Problems Using Systems of Linear Equations
You invested $\$ 28,800$ and started a business selling vases. Supplies cost $\$ 18$ per vase and you are selling each vase for $\$ 34$ . Determine the number of vases, $x$ , that must be produced and sold to break even.

A) 1800 units
B) 1801 units
C) 1802 units
D) 577 units

Question 62

Solve Problems Using Systems of Linear Equations
An-Mei owns a business making and selling jackets. She has a fixed cost of $\$ 1440$ . It costs $\$ 87$ to produce each jacket. The selling price is $\$ 99$ per jacket. Determine the number of jackets that must be made and sold in order to break even.

A) 120 units
B) 121 units
C) 122 units
D) 13 units

Question 63

Solve Problems Using Systems of Linear Equations
Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 800 calories. Three servings of ice cream and two servings of blueberry pie provides 1280 calories. Find the caloric content of each item.

A) Serving of ice cream: 240 calories
B) Serving of ice cream: 280 calories
Serving of blueberry pie: 280 calories Serving of blueberry pie: 240 calories
C) Serving of ice cream: 230 calories
D) Serving of ice cream: 246 calories
Serving of blueberry pie: 285 calories Serving of blueberry pie: 277 calories

Question 64

Solve Problems Using Systems of Linear Equations
As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. The weekly supply and demand models for a certain type of television are as follows:
Demand: $\mathrm { N } = - 4 p + 690$
Supply: $N = 2.6 \mathrm { p }$
where $p$ is the price in dollars per television.
How many of these televisions can be sold and supplied at $\$ 120$ per television?

A) sold: 210 ; supplied: 312
B) sold: 1170 ; supplied: 312
C) sold: 210 ; supplied: 1002
D) sold: 312 ; supplied: 210

Question 65

Solve Problems Using Systems of Linear Equations
A bank teller has $48 \$ 20$ and $\$ 10$ bills in her cash drawer. The value of the bills is $\$ 640$ . How many $\$ 20$ bills are there?

A) $16 \$ 20$ bills
B) $32 \$ 20$ bills
C) $18 \$ 20$ bills
D) $30 \$ 20$ bills

Question 66

Solve Problems Using Systems of Linear Equations
In the town of Milton Lake, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing.
Let $x$ represent the number of years since 1990 and y represent the percentage of women in Milton Lake who smoke. The graph of $y$ against $x$ includes the data points $( 0,16.4 )$ and $( 14,20.32 )$ . Let $x$ represent the number of years since 1990 and y represent the percentage of men in Milton Lake who smoke. The graph of $y$ against $x$ includes the data points $( 0,28.3 )$ and $( 10,26.2 )$ .
Determine when the percentage of women who smoke will be the same as the percentage of men who smoke. Round to the nearest year. What percentage of women and what percentage of men (to the nearest whole percent) will smoke at that time?
[Hint: first find the slope-intercept equation of the line that models the percentage, $\mathrm { y }$ , of women who smoke x years after 1990 and the slope-intercept equation of the line that models the percentage, $y$ , of men who smoke x years after 1990]

A) $2014 ; 23 \%$
B) $2018 ; 22 \%$
C) $2012 ; 24 \%$
D) $2016 ; 23 \%$

Question 67

Solve Problems Using Systems of Linear Equations
A flat rectangular piece of aluminum has a perimeter of 70 inches. The length is 11 inches longer than the width. Find the width.

A) 12 inches
B) 23 inches
C) 34 inches
D) 35 inches

Question 68

Systems of Linear Equations in Three Variables
1 Verify the Solution of a System of Linear Equations in Three Variables
$$\begin{array} { l } ( - 1,5,1 ) \\x + y + z = 5 \\x - y + 5 z = - 1 \\2 x + y + z = 4\end{array}$$

A) solution
B) not a solution

Question 69

Solve Problems Using Systems of Linear Equations
You invested $\$ 13,200$ and started a business selling vases. Supplies cost $\$ 20$ per vase and you are selling each vase for $\$ 31$ . Let $x$ represent the number of vases produced and sold and write the cost function, $C$ , and revenue function, $R$ .

A) $C ( x ) = 20 x + 13,200$
$\mathrm { R } ( \mathrm { x } ) = 31 \mathrm { x }$
B) $C ( x ) = 20 x + 31$
$\mathrm { R } ( \mathrm { x } ) = 13,200 \mathrm { x }$
C) $C ( x ) = 20 x + 13,200$
$R ( x ) = 31$
D) $C ( x ) = 20 x + 13,200 x$

$R ( x ) = 31 x$

Question 70

Solve Problems Using Systems of Linear Equations
A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 3 bags of potato chips for $\$ 12.75$ . Another customer buys 2 hot dogs and 2 bags of potato chips for $\$ 7.00$ . Find the cost of each item.

A) $\$ 2.25$ for a hot dog; $\$ 1.25$ for a bag of potato chips
B) $\$ 1.25$ for a hot dog; $\$ 2.25$ for a bag of potato chips
C) $\$ 2.50$ for a hot dog; $\$ 1.50$ for a bag of potato chips
D) $\$ 2.25$ for a hot dog; $\$ 1.50$ for a bag of potato chips

Question 71

Solve Problems Using Systems of Linear Equations
Julie and Eric row their boat (at a constant speed) 27 miles downstream for 3 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 9 hours. Find the rate of the current.

A) $3 \mathrm { mph }$
B) $6 \mathrm { mph }$
C) $4 \mathrm { mph }$
D) $2.5 \mathrm { mph }$

Question 72

Solve Problems Using Systems of Linear Equations
Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 9 times as many dimes as nickels, and the value of the dimes is $\$ 10.20$ more than the value of the nickels. How many nickels and dimes does Jamil have?

A) 12 nickels and 108 dimes
B) 13 nickels and 117 dimes
C) 11 nickels and 99 dimes
D) 108 nickels and 12 dimes

Question 73

Solve Problems Using Systems of Linear Equations
A rectangular lot whose perimeter is 400 feet is fenced along three sides. An expensive fencing along the lot's length costs $\$ 21$ per foot, and an inexpensive fencing along the two side widths costs only $\$ 10$ per foot. The total cost of the fencing along the three sides comes to $\$ 4140$ . What are the lot's dimensions?

A) Length $140 \mathrm { ft }$ ; Width $60 \mathrm { ft }$
B) Length $143 \mathrm { ft }$ ; Width $57 \mathrm { ft }$
C) Length $135 \mathrm { ft }$ ; Width $65 \mathrm { ft }$
D) Length $280 \mathrm { ft }$ ; Width $120 \mathrm { ft }$

Question 74

Solve Problems Using Systems of Linear Equations
In 1985, in the town of Appleby, $20.3 \%$ of Hispanics were overweight, increasing by an average of $0.43 \%$ per year. In 1985, in the town of Appleby, $0.18 \%$ of whites were overweight, increasing by an average of $31.6 \%$ per year. If these trends continue, in which year will the percentage of Hispanics who are overweight be the same as the percentage of whites who are overweight? Round to the nearest year. What percentage of Hispanics (to the nearest whole percent) will be overweight at that time?

A) $1986 ; 21 \%$
B) $1988 ; 21 \%$
C) $1984 ; 20 \%$
D) $1982 ; 19 \%$

Question 75

Solve Problems Using Systems of Linear Equations
In 1985, in the town of Appleby, $21.2 \%$ of Hispanics were overweight, increasing by an average of $0.42 \%$ per year. In 1985, in the town of Appleby, $0.17 \%$ of whites were overweight, increasing by an average of $31.0 \%$ per year. Write a function that models the percentage, $y$ , of Hispanics who are overweight x years after 1985. Write a function that models the percentage, $y$ , of whites who are overweight x years after $1985 .$

A) Hispanics: $y = 0.42 x + 21.2$
Whites: $\mathrm { y } = 31.0 \mathrm { x } + 0.17$
B) Hispanics: $y = 21.2 x + 0.42$

Whites: $\mathrm { y } = 0.17 \mathrm { x } + 31.0$
C) Hispanics: $\mathrm { y } = 21.62 \mathrm { x }$
Whites: $y = 31.17 x$

D) Hispanics: $y + 0.42 x = 21.2$

Whites: $\mathrm { y } + 31.0 \mathrm { x } = 0.17$

Question 76

Solve Problems Using Systems of Linear Equations
A twin-engined aircraft can fly 1330 miles from city A to city B in 5 hours with the wind and make the return trip in 7 hours against the wind. What is the speed of the wind?

A) $38 \mathrm { mph }$
B) $19 \mathrm { mph }$
C) $57 \mathrm { mph }$
D) $76 \mathrm { mph }$

Question 77

Solve Problems Using Systems of Linear Equations
As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. The weekly supply and demand models for a certain type of television are as follows:
Demand: $\mathrm { N } = - 3 \mathrm { p } + 780$
Supply: $\quad N = 2.5 p$
where $\mathrm { p }$ is the price in dollars per television.
Find the price at which supply and demand are equal. At this price, how many televisions can be supplied and sold each week?

A) $\$ 141.82 ; 355$
B) $\$ 1560.00 ; 3900$
C) $\$ 310.80 ; 777$
D) $\$ 141.82 ; 362$

Question 78

Solve Problems Using Systems of Linear Equations
Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 11 feet more than 5 times the width. He needs 70 feet of fencing to do the job. Find the length and width of the garden.

A) length: 31 feet; width: 4 feet
B) length: $60 \frac { 1 } { 6 }$ feet; width: $9 \frac { 5 } { 6 }$ feet
C) length: 36 feet; width: 5 feet
D) length: 26 feet; width: 3 feet

Question 79

Solve Problems Using Systems of Linear Equations
The Family Fine Arts Center charges $\$ 25$ per adult and $\$ 15$ per senior citizen for its performances. On a recent weekend evening when 502 people paid admission, the total receipts were $\$ 9330$ . How many who paid were senior citizens?

A) 322 senior citizens
B) 180 senior citizens
C) 232 senior citizens
D) 270 senior citizens

Question 80

Solve Problems Using Systems of Linear Equations
In Miguel's home town, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing. The function $y = 0.27 x + 14.2$ models the percentage, $y$ , of women in this city who smoke x years after 1990 . The function $0.20 \mathrm { x } + \mathrm { y } = 29.7$ models the percentage, $\mathrm { y }$ , of men in this city who smoke x years after 1990 . Use these models to determine when the percentage of women who smoke will be the same as the percentage of men who smoke. Round to the nearest year. What percentage of women and what percentage of men (to the nearest whole percent) will smoke at that time?

A) $2023 ; 23 \%$
B) $2024 ; 23 \%$
C) $2022 ; 23 \%$
D) $2025 ; 23 \%$