Question 1

Solve the system by any method.
-$$\left\{ \begin{array} { l } 
9 x + 6 y = - 27 \
8 x - 8 y = 96
\end{array} \right.$$

Accepted Answer

A)  $\varnothing$ 
B)  $( 3 , - 9 )$ 
C)  $( - 3 , - 8 )$ 
D)  $( 2 , - 8 )$ 
A)  $\varnothing$ 
B)  $( 3 , - 9 )$ 
C)  $( - 3 , - 8 )$ 
D)  $( 2 , - 8 )$

Question 2

Solve the problem.
-A company's expenses included many factors. In 2012, travel costs were 2.97% of the expense budget , increasing by 0.21% of the total expense budget per year. In 2012, office supplies were 5.80% of the expense budget, increasing by 0.03% of the total expense budget per year. In which year will the cost of travel expenses and office supplies be the same? For that year, what will be the cost of each expense as a percentage of the total expense budget?

Accepted Answer

A)  2030; 6.8 
B)  2028; 6.3 
C)  2027; 6.1 
D)  2026; 5.9 
A)  2030; 6.8 
B)  2028; 6.3 
C)  2027; 6.1 
D)  2026; 5.9

Question 3

Solve the problem.
-One number is 3 less than a second number. Twice the second number is 2 less than 4 times the first. Find the two numbers.

Accepted Answer

A)  4 and 7 
B)  5 and 8 
C)  -7 and -4 
D)  3 and 6 
A)  4 and 7 
B)  5 and 8 
C)  -7 and -4 
D)  3 and 6

Question 4

Solve the problem.
-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 10 feet more than 2 times the width. He needs 68 feet of fencing to do the job. Find the length and width of the garden.

Accepted Answer

A)  length: $26 \mathrm { ft }$; width: $8 \mathrm { ft }$ 
B)  length: $24 \mathrm { ft }$; width: $7 \mathrm { ft }$ 
C)  length: $48 \frac { 2 } { 3 } \mathrm { ft }$; width: $19 \frac { 1 } { 3 } \mathrm { ft }$ 
D)  length: $28 \mathrm { ft }$; width: $9 \mathrm { ft }$ 
A)  length: $26 \mathrm { ft }$; width: $8 \mathrm { ft }$ 
B)  length: $24 \mathrm { ft }$; width: $7 \mathrm { ft }$ 
C)  length: $48 \frac { 2 } { 3 } \mathrm { ft }$; width: $19 \frac { 1 } { 3 } \mathrm { ft }$ 
D)  length: $28 \mathrm { ft }$; width: $9 \mathrm { ft }$

Question 5

Solve the system by the addition method.
-$$\left\{ \begin{array} { r } 
3 x + y = 10 \
12 x + 4 y = 40
\end{array} \right.$$

Accepted Answer

A)  $\{ ( 0,10 ) \}$ 
B)  $\varnothing$ 
C)  $\{ ( 5 , - 5 ) \}$ 
D)  $\{ ( x , y ) \mid 3 x + y = 10 \}$ 
A)  $\{ ( 0,10 ) \}$ 
B)  $\varnothing$ 
C)  $\{ ( 5 , - 5 ) \}$ 
D)  $\{ ( x , y ) \mid 3 x + y = 10 \}$

Question 6

Solve the system. If there is no solution or if the system's equations are dependent, so state.
-$$\left\{ \begin{array} { r } 
x + 5 y + 2 z = 5 \
2 y + 5 z = - 6 \
z = - 2
\end{array} \right.$$

Accepted Answer

A)  infinitely many solutions; dependent equations 
B)  no solution or $\varnothing$ 
C)  $\{ ( - 1,2 , - 2 ) \}$ 
D)  $\{ ( - 1 , - 2,2 ) \}$ 
A)  infinitely many solutions; dependent equations 
B)  no solution or $\varnothing$ 
C)  $\{ ( - 1,2 , - 2 ) \}$ 
D)  $\{ ( - 1 , - 2,2 ) \}$

Question 7

Solve the system by the addition method.
-$$\left\{ \begin{array} { l } 
3 x + 6 y = 3 \
2 x + 9 y = - 8
\end{array} \right.$$

Accepted Answer

A)  $\{ ( - 5,2 ) \}$ 
B)  $\{ ( x , y ) \mid 3 x + 6 y = 3 \}$ 
C)  $\{ ( 5 , - 2 ) \}$ 
D)  $\varnothing$ 
A)  $\{ ( - 5,2 ) \}$ 
B)  $\{ ( x , y ) \mid 3 x + 6 y = 3 \}$ 
C)  $\{ ( 5 , - 2 ) \}$ 
D)  $\varnothing$

Question 8

Solve the system by the addition method.
-$$\left\{ \begin{array} { l } 
3 x + y = 14 \
3 x + y = 26
\end{array} \right.$$

Accepted Answer

A)  $\{ ( x , y ) \mid 3 x + y = 14 \}$ 
B)  $\varnothing$ 
C)  $\{ ( 12,2 ) \}$ 
D)  $\{ ( 8,11 ) \}$ 
A)  $\{ ( x , y ) \mid 3 x + y = 14 \}$ 
B)  $\varnothing$ 
C)  $\{ ( 12,2 ) \}$ 
D)  $\{ ( 8,11 ) \}$

Question 9

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.

-At the break-even point both cost and revenue are what?

Accepted Answer

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

Question 10

Solve the system by the substitution method.
-$$\left\{ \begin{aligned}
y & = - 3 x + 13 \
2 x + 9 y & = - 8
\end{aligned} \right.$$

Accepted Answer

A)  $\{ ( - 5,2 ) \}$ 
B)  $\varnothing$ 
C)  $\{ ( 5 , - 2 ) \}$ 
D)  $\{ ( x , y ) \mid 3 x + y = 13 \}$ 
A)  $\{ ( - 5,2 ) \}$ 
B)  $\varnothing$ 
C)  $\{ ( 5 , - 2 ) \}$ 
D)  $\{ ( x , y ) \mid 3 x + y = 13 \}$

Question 11

Solve the problem.
-Julie and Eric row their boat (at a constant speed) 24 miles downstream for 4 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 6 hours. Find the rate of the current.

Accepted Answer

A)  2 mph 
B)  1 mph 
C)  0.5 mph 
D)  5 mph 
A)  2 mph 
B)  1 mph 
C)  0.5 mph 
D)  5 mph

Question 12

Solve the system. If there is no solution or if the system's equations are dependent, so state.
-$$\left\{ \begin{array} { l } 
x - y + z = 4 \
x + y + z = - 4 \
x + y - z = 0
\end{array} \right.$$

Accepted Answer

A)  no solution or $\varnothing$ 
B)  infinitely many solutions; dependent equations 
C)  $\{ ( 2 , - 4 , - 2 ) \}$ 
D)  $\{ ( 2 , - 2 , - 4 ) \}$ 
A)  no solution or $\varnothing$ 
B)  infinitely many solutions; dependent equations 
C)  $\{ ( 2 , - 4 , - 2 ) \}$ 
D)  $\{ ( 2 , - 2 , - 4 ) \}$

Question 13

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.

-Use the revenue and cost functions to write the profit function from producing and selling x binoculars.

Accepted Answer

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

Question 14

Solve the problem.
-Given the cost function, C(x), and the revenue function, R(x), write the profit function from producing and selling x units of the product. $$\begin{array} { l } 
C ( x ) = 6000 x + 24,000 \
R ( x ) = 8000 x
\end{array}$$

Accepted Answer

A)  $P ( x ) = 2000 x - 24,000$ 
B)  $P ( x ) = - 2000 x + 24,000$ 
C)  $\mathrm { P } ( \mathrm { x } ) = - 2000 \mathrm { x } - 24,000$ 
D)  $P ( x ) = 2000 x + 24,000$ 
A)  $P ( x ) = 2000 x - 24,000$ 
B)  $P ( x ) = - 2000 x + 24,000$ 
C)  $\mathrm { P } ( \mathrm { x } ) = - 2000 \mathrm { x } - 24,000$ 
D)  $P ( x ) = 2000 x + 24,000$

Question 15

Determine if the given ordered triple is a solution of the system.
-$$\left\{ \begin{array} { l } 
( 1 , - 2,4 ) \
3 x + 5 y + z = - 3 \
2 x - 3 y - z = 4 \
2 x + y + 5 z = 20
\end{array} \right.$$

Accepted Answer

A)  $\text {  solution }$ 
B)  not a solution 
A)  $\text {  solution }$ 
B)  not a solution

Question 16

Solve the system by graphing.
-

Accepted Answer

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

Question 17

Determine whether the system is inconsistent, dependent, or neither.
-$$\left\{ \begin{array} { l } 
3 x + y = 11 \
- 2 y - 4 z = - 24 \
6 x - 2 y - 8 z = - 26
\end{array} \right.$$

Accepted Answer

A)  inconsistent 
B)  neither 
C)  dependent 
A)  inconsistent 
B)  neither 
C)  dependent

Question 18

Solve the system by any method.
-$$\left\{ \begin{array} { l } 
- 3 x + 2 y = 2 \
4 y = 4 + 6 x
\end{array} \right.$$

Accepted Answer

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

Question 19

Solve the problem.
-A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 5 hot dogs, 5 bags of potato chips, and 2 soft drinks for $11.50. The price of a hot dog is $1.00 more than the price of a bag of potato chips. The cost of a soft drink is $2.25 less than the price of two hot dogs. Find the cost of each item.

Accepted Answer

A)  $0.50 for a hot dog; $1.50 for a bag of potato chips; $0.75 for a soft drink 
B)  $1.50 for a hot dog; $0.75 for a bag of potato chips; $0.50 for a soft drink 
C)  $1.50 for a hot dog; $0.50 for a bag of potato chips; $0.75 for a soft drink 
D)  $1.75 for a hot dog; $0.75 for a bag of potato chips; $0.75 for a soft drink 
A)  $0.50 for a hot dog; $1.50 for a bag of potato chips; $0.75 for a soft drink 
B)  $1.50 for a hot dog; $0.75 for a bag of potato chips; $0.50 for a soft drink 
C)  $1.50 for a hot dog; $0.50 for a bag of potato chips; $0.75 for a soft drink 
D)  $1.75 for a hot dog; $0.75 for a bag of potato chips; $0.75 for a soft drink

Question 20

Solve the problem.
-Given the cost function, $C ( x )$, and the revenue function, $R ( x )$, find the dollar amount coming in and going out at the break-even point. Round to the nearest dollar if necessary.
$$\begin{array} { l } 
C ( x ) = 1.7 x + 700 \
R ( x ) = 2.7 x
\end{array}$$

Accepted Answer

A)  $\$ 700$ 
B)  $\$ 1890$ 
C)  $\$ 266$ 
D)  $\$ 430$ 
A)  $\$ 700$ 
B)  $\$ 1890$ 
C)  $\$ 266$ 
D)  $\$ 430$

Solve the system by any method. - $\left\{ \begin{array} { l } 9 x + 6 y = - 27 \\8 x - 8 y = 96\end{array} \right.$

Solve the problem. -One number is 3 less than a second number. Twice the second number is 2 less than 4 times the first. Find the two numbers.

Solve the problem. -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 10 feet more than 2 times the width. He needs 68 feet of fencing to do the job. Find the length and width of the garden.

Solve the system by the addition method. - $\left\{ \begin{array} { r } 3 x + y = 10 \\12 x + 4 y = 40\end{array} \right.$

Solve the system. If there is no solution or if the system's equations are dependent, so state. - $\left\{ \begin{array} { r } x + 5 y + 2 z = 5 \\2 y + 5 z = - 6 \\z = - 2\end{array} \right.$

Solve the system by the addition method. - $\left\{ \begin{array} { l } 3 x + 6 y = 3 \\2 x + 9 y = - 8\end{array} \right.$

Solve the system by the addition method. - $\left\{ \begin{array} { l } 3 x + y = 14 \\3 x + y = 26\end{array} \right.$

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. -At the break-even point both cost and revenue are what?

Solve the system by the substitution method. - $\left\{ \begin{aligned}y & = - 3 x + 13 \\2 x + 9 y & = - 8\end{aligned} \right.$

Solve the problem. -Julie and Eric row their boat (at a constant speed) 24 miles downstream for 4 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 6 hours. Find the rate of the current.

Solve the system. If there is no solution or if the system's equations are dependent, so state. - $\left\{ \begin{array} { l } x - y + z = 4 \\x + y + z = - 4 \\x + y - z = 0\end{array} \right.$

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. -Use the revenue and cost functions to write the profit function from producing and selling x binoculars.

Solve the problem. -Given the cost function, C(x), and the revenue function, R(x), write the profit function from producing and selling x units of the product. C(x)=6000x+24,000 R(x)=8000x

Determine if the given ordered triple is a solution of the system. - $\left\{ \begin{array} { l } ( 1 , - 2,4 ) \\3 x + 5 y + z = - 3 \\2 x - 3 y - z = 4 \\2 x + y + 5 z = 20\end{array} \right.$

Solve the system by graphing. -

Determine whether the system is inconsistent, dependent, or neither. - $\left\{ \begin{array} { l } 3 x + y = 11 \\- 2 y - 4 z = - 24 \\6 x - 2 y - 8 z = - 26\end{array} \right.$

Solve the system by any method. - $\left\{ \begin{array} { l } - 3 x + 2 y = 2 \\4 y = 4 + 6 x\end{array} \right.$

Solve the problem. -Given the cost function, $C ( x )$ , and the revenue function, $R ( x )$ , find the dollar amount coming in and going out at the break-even point. Round to the nearest dollar if necessary. C(x)=1.7x+700 R(x)=2.7x

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Exam 3: Systems of Linear Equations

Solve the system by any method. - {9x+6y=−278x−8y=96\left\{ \begin{array} { l } 9 x + 6 y = - 27 \\8 x - 8 y = 96\end{array} \right.{9x+6y=−278x−8y=96​