Question 1

Solve the problem.
-Given the cost function, $C ( x )$, and the revenue function, $R ( x )$, find the number of units $x$ that must be sold to brea
$$\begin{array} { l } 
C ( x ) = 14 x + 24,000 \
R ( x ) = 34 x
\end{array}$$

Accepted Answer

A)  1200 units 
B)  445 units 
C)  1201 units 
D)  1202 units en. 
A)  1200 units 
B)  445 units 
C)  1201 units 
D)  1202 units en.

Question 2

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.

-More than how many binoculars must be produced and sold for the company to have a profit gain?

Accepted Answer

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

Question 3

Solve the system by graphing.
-$$\left\{ \begin{aligned}
y - 6 x & = 5 \
6 y & = 36 x + 30
\end{aligned} \right.$$

Accepted Answer

A)  $\{ ( 1,1 ) \}$ 
B)  $\varnothing$ 
C)  $\{ ( - 1.5 , - 1 ) \}$ 
D)  $\{ ( x , y ) \mid y - 6 x = 5 \}$ 
A)  $\{ ( 1,1 ) \}$ 
B)  $\varnothing$ 
C)  $\{ ( - 1.5 , - 1 ) \}$ 
D)  $\{ ( x , y ) \mid y - 6 x = 5 \}$

Question 4

Determine whether the system is inconsistent, dependent, or neither.
-$$\left\{ \begin{array} { l } 
x + y + z = 1 \
x - y + 2 z = - 8 \
2 x + 2 y + 2 z = - 1
\end{array} \right.$$

Accepted Answer

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

Question 5

Solve the system by any method.
-$$\left\{ \begin{array} { l } 
8 x - 82 = - 6 y \
6 x + 4 y = 60
\end{array} \right.$$

Accepted Answer

A)  $\{ ( x , y ) \mid 8 x - 82 = - 6 y \}$ 
B)  $( 8,4 )$ 
C)  $( 8,3 )$ 
D)  $( 7,4 )$ 
A)  $\{ ( x , y ) \mid 8 x - 82 = - 6 y \}$ 
B)  $( 8,4 )$ 
C)  $( 8,3 )$ 
D)  $( 7,4 )$

Question 6

Solve the system by the addition method.
-$$\left\{ \begin{array} { l } 
5 x + 7 y = 54 \
5 x + 2 y = 69
\end{array} \right.$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ ( - 15,5 ) \}$ 
C)  $\{ ( 15 , - 3 ) \}$ 
D)  $\{ ( x , y ) \mid 5 x + 2 y = 69 \}$ 
A)  $\varnothing$ 
B)  $\{ ( - 15,5 ) \}$ 
C)  $\{ ( 15 , - 3 ) \}$ 
D)  $\{ ( x , y ) \mid 5 x + 2 y = 69 \}$

Question 7

Determine if the given ordered triple is a solution of the system.
-$$\left\{ \begin{array} { c } 
( 0 , - 4 , - 3 ) \
3 x - y + 5 z = - 11 \
x + z = - 3 \
x + 2 y + z = - 11
\end{array} \right.$$

Accepted Answer

A)  not a solution 
B)  solution 
A)  not a solution 
B)  solution

Question 8

Determine whether the system is inconsistent, dependent, or neither.
-$$\left\{ \begin{array} { l } 
x - y + 2 z = - 5 \
3 x + z = 0 \
- x + y - 2 z = 20
\end{array} \right.$$

Accepted Answer

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

Question 9

Solve the problem.
-Given the cost function, $C ( x )$, and the revenue function, $R ( x )$, find the number of units $x$ that must be sold to brea
$$\begin{array} { l } 
C ( x ) = 1.3 x + 840 \
R ( x ) = 1.9 x
\end{array}$$

Accepted Answer

A)  1400 units 
B)  1420 units 
C)  337 units 
D)  1410 units en. 
A)  1400 units 
B)  1420 units 
C)  337 units 
D)  1410 units en.

Question 10

Solve the system by the addition method.
-$$\left\{ \begin{array} { l } 
3 x - 5 y = - 12 \
6 x + 8 y = - 24
\end{array} \right.$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ ( 4,0 ) \}$ 
C)  $\{ ( - 4,0 ) \}$ 
D)  $\{ ( x , y ) \mid 3 x - 5 y = - 12 \}$ 
A)  $\varnothing$ 
B)  $\{ ( 4,0 ) \}$ 
C)  $\{ ( - 4,0 ) \}$ 
D)  $\{ ( x , y ) \mid 3 x - 5 y = - 12 \}$

Question 11

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

Accepted Answer

A)  not a solution 
B)  solution 
A)  not a solution 
B)  solution

Question 12

Solve the system. If there is no solution or if the system's equations are dependent, so state.
-$$\left\{ \begin{array} { r r } 
x + y + z = & 2 \
x - y - 2 z = & - 10 \
3 x + 3 y + 3 z = & 6
\end{array} \right.$$

Accepted Answer

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

Question 13

Solve the problem.
-A flat rectangular piece of aluminum has a perimeter of 56 inches. The length is 6 inches longer than the width. Find the width.

Accepted Answer

A)  11 in. 
B)  28 in. 
C)  17 in. 
D)  23 in. 
A)  11 in. 
B)  28 in. 
C)  17 in. 
D)  23 in.

Question 14

Solve the problem.
-One number is 4 less than a second number. Twice the second number is 17 more than 3 times the first. Find the two numbers.

Accepted Answer

A)  5 and 9 
B)  -10 and -6 
C)  -8 and -4 
D)  -9 and -5 
A)  5 and 9 
B)  -10 and -6 
C)  -8 and -4 
D)  -9 and -5

Question 15

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.

-Fewer than how many binoculars must be produced and sold for the company to have a profit loss?

Accepted Answer

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

Question 16

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.
$$\begin{array} { l } 
C ( x ) = 8000 x + 90,000 \
R ( x ) = 17,000 x
\end{array}$$

Accepted Answer

A)  $\$ 170,000$ 
B)  $\$ 10$ 
C)  $\$ 80,000$ 
D)  $\$ 61,200$ 
A)  $\$ 170,000$ 
B)  $\$ 10$ 
C)  $\$ 80,000$ 
D)  $\$ 61,200$

Question 17

Determine if the given ordered triple is a solution of the system.
-$$\left\{ \begin{array} { l } 
5 , - 2,3 ) \
x + y + z = 6 \
x - y + 4 z = 19 \
5 x + y + z = 26
\end{array} \right.$$

Accepted Answer

A)  solution 
B)  not a solution 
A)  solution 
B)  not a solution

Question 18

Solve the system by the substitution method.
-$$\left\{ \begin{array} { r } 
x + 7 y = - 2 \
3 x + y = 34
\end{array} \right.$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ ( x , y ) \mid x + 7 y = - 2 \}$ 
C)  $\{ ( 12 , - 2 ) \}$ 
D)  $\{ ( - 2,3 ) \}$ 
A)  $\varnothing$ 
B)  $\{ ( x , y ) \mid x + 7 y = - 2 \}$ 
C)  $\{ ( 12 , - 2 ) \}$ 
D)  $\{ ( - 2,3 ) \}$

Question 19

Solve the system by the substitution method.
-$$\left\{ \begin{array} { l } 
\frac { x } { 3 } - \frac { y } { 6 } = 1 \
\frac { x } { 7 } - y = 6
\end{array} \right.$$

Accepted Answer

A)  $( - 6,0 )$ 
B)  $( 0 , - 6 )$ 
C)  $( 6,0 )$ 
D)  $( 0,6 )$ 
A)  $( - 6,0 )$ 
B)  $( 0 , - 6 )$ 
C)  $( 6,0 )$ 
D)  $( 0,6 )$

Question 20

Solve the problem.
-A bank teller has 53 $20 and $5 bills in her cash drawer. The value of the bills is $490. How many $20 bills are there?

Accepted Answer

A)  38 $20 bills 
B)  36 $20 bills 
C)  17 $20 bills 
D)  15 $20 bills 
A)  38 $20 bills 
B)  36 $20 bills 
C)  17 $20 bills 
D)  15 $20 bills

Solve the problem. -Given the cost function, $C ( x )$ , and the revenue function, $R ( x )$ , find the number of units $x$ that must be sold to brea C(x)=14x+24,000 R(x)=34x

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. -More than how many binoculars must be produced and sold for the company to have a profit gain?

Solve the system by graphing. - $\left\{ \begin{aligned}y - 6 x & = 5 \\6 y & = 36 x + 30\end{aligned} \right.$ $Solve the system by graphing. - \left\{ \begin{aligned} y - 6 x & = 5 \\ 6 y & = 36 x + 30 \end{aligned} \right.$

Determine whether the system is inconsistent, dependent, or neither. - $\left\{ \begin{array} { l } x + y + z = 1 \\x - y + 2 z = - 8 \\2 x + 2 y + 2 z = - 1\end{array} \right.$

Solve the system by any method. - $\left\{ \begin{array} { l } 8 x - 82 = - 6 y \\6 x + 4 y = 60\end{array} \right.$

Solve the system by the addition method. - $\left\{ \begin{array} { l } 5 x + 7 y = 54 \\5 x + 2 y = 69\end{array} \right.$

Determine if the given ordered triple is a solution of the system. - $\left\{ \begin{array} { c } ( 0 , - 4 , - 3 ) \\3 x - y + 5 z = - 11 \\x + z = - 3 \\x + 2 y + z = - 11\end{array} \right.$

Determine whether the system is inconsistent, dependent, or neither. - $\left\{ \begin{array} { l } x - y + 2 z = - 5 \\3 x + z = 0 \\- x + y - 2 z = 20\end{array} \right.$

Solve the problem. -Given the cost function, $C ( x )$ , and the revenue function, $R ( x )$ , find the number of units $x$ that must be sold to brea C(x)=1.3x+840 R(x)=1.9x

Solve the system by the addition method. - $\left\{ \begin{array} { l } 3 x - 5 y = - 12 \\6 x + 8 y = - 24\end{array} \right.$

Determine whether the given ordered pair is a solution to the system. - (6,2) y=2 x=3y

Solve the system. If there is no solution or if the system's equations are dependent, so state. - $\left\{ \begin{array} { r r } x + y + z = & 2 \\x - y - 2 z = & - 10 \\3 x + 3 y + 3 z = & 6\end{array} \right.$

Solve the problem. -A flat rectangular piece of aluminum has a perimeter of 56 inches. The length is 6 inches longer than the width. Find the width.

Solve the problem. -One number is 4 less than a second number. Twice the second number is 17 more than 3 times the first. Find the two numbers.

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. -Fewer than how many binoculars must be produced and sold for the company to have a profit loss?

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)=8000x+90,000 R(x)=17,000x

Determine if the given ordered triple is a solution of the system. - $\left\{ \begin{array} { l } 5 , - 2,3 ) \\x + y + z = 6 \\x - y + 4 z = 19 \\5 x + y + z = 26\end{array} \right.$

Solve the system by the substitution method. - $\left\{ \begin{array} { r } x + 7 y = - 2 \\3 x + y = 34\end{array} \right.$

Solve the system by the substitution method. - $\left\{ \begin{array} { l } \frac { x } { 3 } - \frac { y } { 6 } = 1 \\\frac { x } { 7 } - y = 6\end{array} \right.$

Solve the problem. -A bank teller has 53 $20 and $5 bills in her cash drawer. The value of the bills is $490. How many $20 bills are there?

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Exam 3: Systems of Linear Equations

Solve the problem. -Given the cost function, C(x)C ( x )C(x) , and the revenue function, R(x)R ( x )R(x) , find the number of units xxx that must be sold to brea C(x)=14x+24,000 R(x)=34x

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. -More than how many binoculars must be produced and sold for the company to have a profit gain?

Solve the system by graphing. - {y−6x=56y=36x+30\left\{ \begin{aligned}y - 6 x & = 5 \\6 y & = 36 x + 30\end{aligned} \right.{y−6x6y​=5=36x+30​

Determine whether the system is inconsistent, dependent, or neither. - {x+y+z=1x−y+2z=−82x+2y+2z=−1\left\{ \begin{array} { l } x + y + z = 1 \\x - y + 2 z = - 8 \\2 x + 2 y + 2 z = - 1\end{array} \right.⎩⎨⎧​x+y+z=1x−y+2z=−82x+2y+2z=−1​

Solve the system by any method. - {8x−82=−6y6x+4y=60\left\{ \begin{array} { l } 8 x - 82 = - 6 y \\6 x + 4 y = 60\end{array} \right.{8x−82=−6y6x+4y=60​

Solve the system by the addition method. - {5x+7y=545x+2y=69\left\{ \begin{array} { l } 5 x + 7 y = 54 \\5 x + 2 y = 69\end{array} \right.{5x+7y=545x+2y=69​

Determine whether the system is inconsistent, dependent, or neither. - {x−y+2z=−53x+z=0−x+y−2z=20\left\{ \begin{array} { l } x - y + 2 z = - 5 \\3 x + z = 0 \\- x + y - 2 z = 20\end{array} \right.⎩⎨⎧​x−y+2z=−53x+z=0−x+y−2z=20​

Solve the problem. -Given the cost function, C(x)C ( x )C(x) , and the revenue function, R(x)R ( x )R(x) , find the number of units xxx that must be sold to brea C(x)=1.3x+840 R(x)=1.9x

Solve the system by the addition method. - {3x−5y=−126x+8y=−24\left\{ \begin{array} { l } 3 x - 5 y = - 12 \\6 x + 8 y = - 24\end{array} \right.{3x−5y=−126x+8y=−24​