Question 1

Solve.
-One number is 3 less than a second number. Twice the second number is 21 less than 5 times the first. Find the two numbers.

Accepted Answer

A)  9 and 12 
B)  $- 12$ and $- 9$ 
C)  10 and 13 
D)  8 and 11 
A)  9 and 12 
B)  $- 12$ and $- 9$ 
C)  10 and 13 
D)  8 and 11

Question 2

Solve the system of equations.
-$$\left\{ \begin{array} { r } 
\frac { 3 } { 10 } x + \frac { 1 } { 2 } y = \frac { 47 } { 10 } \
3 x + 2 y = 53
\end{array} \right.$$

Accepted Answer

A)  $( 19 , - 2 )$ 
B)  $( - 19,3 )$ 
C)  $( - 2,19 )$ 
D)  $( - 19,5 )$ 
A)  $( 19 , - 2 )$ 
B)  $( - 19,3 )$ 
C)  $( - 2,19 )$ 
D)  $( - 19,5 )$

Question 3

Solve the system of equations.
-$$\left\{ \begin{aligned}
3 y & = x + 18 \
3 x + 9 y & = 0
\end{aligned} \right.$$

Accepted Answer

A)  $( 3 , - 9 )$ 
B)  $( - 9,3 )$ 
C)  $\{ ( x , y ) \mid 3 y = x + 18 \}$ 
D)  $\varnothing$ 
A)  $( 3 , - 9 )$ 
B)  $( - 9,3 )$ 
C)  $\{ ( x , y ) \mid 3 y = x + 18 \}$ 
D)  $\varnothing$

Question 4

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l } 
\text { matrix consistent system of equations triple } \
\text { solution inconsistent element } \
\text { column }
\end{array}$$
-A(n) of a system of two equations in two variables is an ordered pair that makes both equations true.

Accepted Answer

A)  solution 
B)  system of equations 
C)  matrix 
D)  column 
A)  solution 
B)  system of equations 
C)  matrix 
D)  column

Question 5

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
-$$\begin{array} { l } 
C ( x ) = 143 x + 306,000 \
R ( x ) = 313 x
\end{array}$$

Accepted Answer

A)  1801 units 
B)  1800 units 
C)  634 units 
D)  1802 units 
A)  1801 units 
B)  1800 units 
C)  634 units 
D)  1802 units

Question 6

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l } 
\text { matrix consistent system of equations triple } \
\text { solution inconsistent element } \
\text { column }
\end{array}$$
-Each of the numbers in a matrix is called a(n) .

Accepted Answer

A)  row 
B)  element 
C)  solution 
D)  column 
A)  row 
B)  element 
C)  solution 
D)  column

Question 7

Solve the system of equations.
-$$\left\{ \begin{aligned}
y & = 4 x + 5 \
4 y + 12 x & = 132
\end{aligned} \right.$$

Accepted Answer

A)  $( 4,21 )$ 
B)  $( 21,4 )$ 
C)  $\{ ( x , y ) \mid y = 4 x + 5 \}$ 
D)  $\varnothing$ 
A)  $( 4,21 )$ 
B)  $( 21,4 )$ 
C)  $\{ ( x , y ) \mid y = 4 x + 5 \}$ 
D)  $\varnothing$

Question 8

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
-Three trains  one eastbound, one westbound, and one northbound  leave a city at the same time. The speed of the northbound train is 10 miles per hour greater than the speed of the eastbound train. After 2 hours, the
Distance between the westbound train and the eastbound train is 200 miles. Twice the speed of the westbound
Train is 100 miles per hour more than the speed of the northbound train. Find the speeds of the three trains.

Accepted Answer

A)  eastbound, 40 mph; westbound, 70 mph; northbound, 30 mph 
B)  eastbound, 20 mph; westbound, 80 mph; northbound, 40 mph 
C)  eastbound, 30 mph; westbound, 70 mph; northbound, 40 mph 
D)  eastbound, 40 mph; westbound, 70 mph; northbound, 50 mph 
A)  eastbound, 40 mph; westbound, 70 mph; northbound, 30 mph 
B)  eastbound, 20 mph; westbound, 80 mph; northbound, 40 mph 
C)  eastbound, 30 mph; westbound, 70 mph; northbound, 40 mph 
D)  eastbound, 40 mph; westbound, 70 mph; northbound, 50 mph

Question 9

Graph the solution of the system of linear inequalities.
-$\left\{\begin{array}{l}
2 x-y \leq 4 \
x+4 y \geq-12
\end{array}\right.$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 10

Solve the system of linear equations using matrices.
-$$\left\{ \begin{array} { l } 
x + 2 y = 5 \
x + 3 y = 8
\end{array} \right.$$

Accepted Answer

A)  $( 3 , - 1 )$ 
B)  $( - 3,1 )$ 
C)  $( - 1,3 )$ 
D)  $\varnothing$ 
A)  $( 3 , - 1 )$ 
B)  $( - 3,1 )$ 
C)  $( - 1,3 )$ 
D)  $\varnothing$

Question 11

Solve the system.
-$\int 4 x + y - \frac { 2 } { 3 } z = 29$
$\left\{ \frac { 1 } { 3 } x - 2 z = 8 \right.$
$x + 2 y = 12$

Accepted Answer

A)  $( - 9,4 , - 2 )$ 
B)  $( 4 , - 3 , - 6 )$ 
C)  $( 6,3 , - 3 )$ 
D)  $( 4,4 , - 3 )$ 
A)  $( - 9,4 , - 2 )$ 
B)  $( 4 , - 3 , - 6 )$ 
C)  $( 6,3 , - 3 )$ 
D)  $( 4,4 , - 3 )$

Question 12

Use matrices to solve the system.
-$$\left\{ \begin{array} { l } 
3 x + 2 y = - 6 \
5 x + 6 y = - 2
\end{array} \right.$$

Accepted Answer

A)  $( 3 , - 4 )$ 
B)  $( - 4 , - 3 )$ 
C)  $( - 4,3 )$ 
D)  $\varnothing$ 
A)  $( 3 , - 4 )$ 
B)  $( - 4 , - 3 )$ 
C)  $( - 4,3 )$ 
D)  $\varnothing$

Question 13

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l } 
\text { matrix consistent system of equations triple } \
\text { solution inconsistent element } \
\text { column }
\end{array}$$
-The numbers aligned vertically in a matrix are in the same .

Accepted Answer

A)  solution 
B)  element 
C)  row 
D)  column 
A)  solution 
B)  element 
C)  row 
D)  column

Question 14

Solve the system of linear equations using matrices.
-$$\left\{ \begin{array} { l } 
2 x + y = 1 \
3 x + y = 3
\end{array} \right.$$

Accepted Answer

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

Question 15

Solve the system.
-$$\left\{ \begin{aligned}
x + y + z & = 7 \
x - y + 5 z & = - 3 \
4 x + y + z & = 22
\end{aligned} \right.$$

Accepted Answer

A)  $( 5,3 , - 1 )$ 
B)  $( - 1,3,5 )$ 
C)  $( - 1,5,3 )$ 
D)  $\varnothing$ 
A)  $( 5,3 , - 1 )$ 
B)  $( - 1,3,5 )$ 
C)  $( - 1,5,3 )$ 
D)  $\varnothing$

Question 16

Solve the system.
-$ \left\{\begin{array}{l}3 x-5 y=-4 \ 5 x+3 y=-18 \ \end{array}\right. $

Accepted Answer

A)  $ (3,1) $ 
B)  $ (-3,1) $ 
C)  $ (-3,-1) $ 
D)  $ (3,-1) $ 
A)  $ (3,1) $ 
B)  $ (-3,1) $ 
C)  $ (-3,-1) $ 
D)  $ (3,-1) $

Question 17

Solve the system.
-$$\left\{ \begin{array} { r } 
y - 4 z = - 10 \
- 2 x + y - 5 z = - 11 \
4 x + 5 z = 11
\end{array} \right.$$

Accepted Answer

A)  $( 4,3 , - 1 )$ 
B)  $( 4 , - 8 , - 1 )$ 
C)  $( - 1,2,3 )$ 
D)  $( - 1,6,4 )$ 
A)  $( 4,3 , - 1 )$ 
B)  $( 4 , - 8 , - 1 )$ 
C)  $( - 1,2,3 )$ 
D)  $( - 1,6,4 )$

Question 18

Write the word or phrase that best completes each statement or answers the question.
The revenue equation for a certain brand of mouthwash is y = 1.3x, where x is the number of bottles of mouthwash sold
and y is the total income for selling x bottles. The cost equation is y = 0.5x + 2500, where x is the number of bottles of
mouthwash manufactured and y is the cost of producing x bottles. The following set of axes shows the graph of the cost
and revenue equations.  
-If the company sells 3500 bottles of mouthwash, does the company make money or lose money?

Accepted Answer

The answer of Write the word or phrase that best...

Question 19

Solve the system of equations by the substitution method.
-$$\left\{ \begin{array} { r } 
x - 5 y = - 10 \
2 x - 6 y = - 8
\end{array} \right.$$

Accepted Answer

A)  $( 4,4 )$ 
B)  $( 5,3 )$ 
C)  $( - 5,4 )$ 
D)  $\varnothing$ 
A)  $( 4,4 )$ 
B)  $( 5,3 )$ 
C)  $( - 5,4 )$ 
D)  $\varnothing$

Question 20

Solve.
-A chemist needs 170 milliliters of a 59% solution but has only 15% and 83% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Accepted Answer

A)  65 ml of 15%; 105 ml of 83% 
B)  65 ml of 15%; 110 ml of 83% 
C)  110 ml of 15%; 60 ml of 83% 
D)  60 ml of 15%; 110 ml of 83% 
A)  65 ml of 15%; 105 ml of 83% 
B)  65 ml of 15%; 110 ml of 83% 
C)  110 ml of 15%; 60 ml of 83% 
D)  60 ml of 15%; 110 ml of 83%

Solve. -One number is 3 less than a second number. Twice the second number is 21 less than 5 times the first. Find the two numbers.

Solve the system of equations. - $\left\{ \begin{array} { r } \frac { 3 } { 10 } x + \frac { 1 } { 2 } y = \frac { 47 } { 10 } \\3 x + 2 y = 53\end{array} \right.$

Solve the system of equations. - $\left\{ \begin{aligned}3 y & = x + 18 \\3 x + 9 y & = 0\end{aligned} \right.$

Fill in the blank with one of the words or phrases listed below. matrix consistent system of equations triple solution inconsistent element column -A(n) of a system of two equations in two variables is an ordered pair that makes both equations true.

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even. - C(x)=143x+306,000 R(x)=313x

Fill in the blank with one of the words or phrases listed below. matrix consistent system of equations triple solution inconsistent element column -Each of the numbers in a matrix is called a(n) .

Solve the system of equations. - $\left\{ \begin{aligned}y & = 4 x + 5 \\4 y + 12 x & = 132\end{aligned} \right.$

Graph the solution of the system of linear inequalities. - $\left\{\begin{array}{l}2 x-y \leq 4 \\x+4 y \geq-12\end{array}\right.$ $Graph the solution of the system of linear inequalities. - \left\{\begin{array}{l} 2 x-y \leq 4 \\ x+4 y \geq-12 \end{array}\right.$

Solve the system of linear equations using matrices. - $\left\{ \begin{array} { l } x + 2 y = 5 \\x + 3 y = 8\end{array} \right.$

Solve the system. - $\int 4 x + y - \frac { 2 } { 3 } z = 29$ $\left\{ \frac { 1 } { 3 } x - 2 z = 8 \right.$ $x + 2 y = 12$

Use matrices to solve the system. - $\left\{ \begin{array} { l } 3 x + 2 y = - 6 \\5 x + 6 y = - 2\end{array} \right.$

Fill in the blank with one of the words or phrases listed below. matrix consistent system of equations triple solution inconsistent element column -The numbers aligned vertically in a matrix are in the same .

Solve the system of linear equations using matrices. - $\left\{ \begin{array} { l } 2 x + y = 1 \\3 x + y = 3\end{array} \right.$

Solve the system. - $\left\{ \begin{aligned}x + y + z & = 7 \\x - y + 5 z & = - 3 \\4 x + y + z & = 22\end{aligned} \right.$

Solve the system. - $\left\{\begin{array}{l}3 x-5 y=-4 \\ 5 x+3 y=-18 \\ \end{array}\right.$

Solve the system. - $\left\{ \begin{array} { r } y - 4 z = - 10 \\- 2 x + y - 5 z = - 11 \\4 x + 5 z = 11\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r } x - 5 y = - 10 \\2 x - 6 y = - 8\end{array} \right.$

Solve. -A chemist needs 170 milliliters of a 59% solution but has only 15% and 83% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 4: Systems of Equations and Inequalities