Question 1

Graph the inequality.
-x - y > -2

Accepted Answer

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

Question 2

Solve the system of equations.
-$$\begin{array} { c } 
x - y + 3 z = - 2 \
3 x + z = 0 \
x + 3 y + z = 6
\end{array}$$

Accepted Answer

A)  $\{ ( 0,2,0 ) \}$ 
B)  $\{ ( 0,0,2 ) \}$ 
C)  $\{ ( 2,0,0 ) \}$ 
D)  $\{ ( 0,2 , - 2 ) \}$ 
A)  $\{ ( 0,2,0 ) \}$ 
B)  $\{ ( 0,0,2 ) \}$ 
C)  $\{ ( 2,0,0 ) \}$ 
D)  $\{ ( 0,2 , - 2 ) \}$

Question 3

Graph the inequality.
-$$y \leq 6$$

Accepted Answer

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

Question 4

Graph the solution set of the system of inequalities or indicate that the system has no solution.
-$\begin{array}{l}
2 x+y>10 \
2 x+y<-1
\end{array}$

Accepted Answer

A)  no solution 
B) 
  
C) 
  
D) 
  
A)  no solution 
B) 
  
C) 
  
D)

Question 5

Graph the solution set of the system of inequalities or indicate that the system has no solution.
-$\begin{array}{l}
4 x-y \leq-4 \
x+2 y \geq 4
\end{array}$

Accepted Answer

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

Question 6

Graph the solution set of the system of inequalities or indicate that the system has no solution.
-$\begin{array}{l}
x \geq 0 \
y \geq 0 \
3 x+3 y \leq 9 \
2 x+y \leq 4
\end{array}$

Accepted Answer

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

Question 7

An objective function and a system of linear inequalities representing constraints are given. Graph the system of
inequalities representing the constraints. Find the value of the objective function at each corner of the graphed
region. Use these values to determine the maximum value of the objective function and the values of x and y for
which the maximum occurs.
-$$\begin{array} { l l } 
\text { Objective Function } & z = 6 x + 7 y \
\text { Constraints } & x \geq 0 \
& y \geq 0 \
& 2 x + 3 y \leq 12 \
& 2 x + y \leq 8
\end{array}$$

Accepted Answer

A) Maximum 32; at (3, 2) 
B) Maximum 32; at (2, 3) 
C) Maximum 52; at (4, 4) 
D) Maximum 24; at (4, 0) 
A) Maximum 32; at (3, 2) 
B) Maximum 32; at (2, 3) 
C) Maximum 52; at (4, 4) 
D) Maximum 24; at (4, 0)

Question 8

Solve the problem.
-The table shows the percentage of people living below the poverty line in one U.S. city in the years 2000 through 2003.

The data in the table can be written as ordered pairs $( x , y )$ where $x$ is the number of years after 2000 and $y$ is the percentage of people living below the poverty line in that year. Use the data for 2000, 2002, and 2003 to find the quadratic function $y = a x ^ { 2 } + b x + c$ that models the percentage, $y$, of people in this city living below the poverty line $x$ years after 2000 .
[Hint: Find $a , b$, and c by substituting each of three ordered pairs into the function and writing and solving a system of linear equations in three variables.]

Accepted Answer

A)  $y = - 0.3 x ^ { 2 } + 1.6 x + 11.7$ 
B)  $y = - 0.4 x ^ { 2 } + 1.8 x + 11.7$ 
C)  $y = - 0.2 x ^ { 2 } + 1.4 x + 11.7$ 
D)  $\mathrm { y } = - 0.4 \mathrm { x } ^ { 2 } + 1.9 \mathrm { x } + 11.7$ 
A)  $y = - 0.3 x ^ { 2 } + 1.6 x + 11.7$ 
B)  $y = - 0.4 x ^ { 2 } + 1.8 x + 11.7$ 
C)  $y = - 0.2 x ^ { 2 } + 1.4 x + 11.7$ 
D)  $\mathrm { y } = - 0.4 \mathrm { x } ^ { 2 } + 1.9 \mathrm { x } + 11.7$

Question 9

Solve the system by the addition method.
-$$\begin{aligned}
x + 6 y & = 11 \
4 x + 5 y & = - 13
\end{aligned}$$

Accepted Answer

A)  $\{ ( - 7,3 ) \}$ 
B)  $\{ ( - 8,4 ) \}$ 
C)  $\{ ( 7,4 ) \}$ 
D)  $\varnothing$ 
A)  $\{ ( - 7,3 ) \}$ 
B)  $\{ ( - 8,4 ) \}$ 
C)  $\{ ( 7,4 ) \}$ 
D)  $\varnothing$

Question 10

Solve the system of equations by the substitution method.
-$$\begin{array} { l } 
6 x + y = - 7 \
3 x - 5 y = - 9
\end{array}$$

Accepted Answer

A)  $\left. \left\{ - \frac { 4 } { 3 } , 1 \right] \right\}$ 
B)  $\{ ( 1,9 ) \}$ 
C)  $\left\{ \left[ - 5 , \frac { 6 } { 5 } \right\} \right\}$ 
D)  $\left\{ \left[ - \frac { 1 } { 3 } , - 5 \right\} \right\}$ 
A)  $\left. \left\{ - \frac { 4 } { 3 } , 1 \right] \right\}$ 
B)  $\{ ( 1,9 ) \}$ 
C)  $\left\{ \left[ - 5 , \frac { 6 } { 5 } \right\} \right\}$ 
D)  $\left\{ \left[ - \frac { 1 } { 3 } , - 5 \right\} \right\}$

Question 11

Graph the inequality.
-x - y < -6

Accepted Answer

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

Question 12

Solve the problem.
-A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given by the equation $h = - 16 t ^ { 2 } + 600$ where $h$ is measured in feet and $t$ is the number of seconds since the yellow ball was dropped. A second person, in the same building but on a lower floor that is 408 feet from the ground, drops a white ball 3 seconds after the yellow ball was dropped. The height of the white ball is given by the equation $\mathrm { h } = - 16 ( \mathrm { t } - 3 ) ^ { 2 } + 408$ where $\mathrm { h }$ is measured in feet and $\mathrm { t }$ is the number of seconds since the yellow ball was dropped. Find the time that the balls are the same distance above the ground and find this distance.

Accepted Answer

A)  $3.5$ seconds; 404 feet 
B)  $2.5$ seconds; 500 feet 
C)  3 seconds; 456 feet 
D)  4 seconds; 344 feet 
A)  $3.5$ seconds; 404 feet 
B)  $2.5$ seconds; 500 feet 
C)  3 seconds; 456 feet 
D)  4 seconds; 344 feet

Question 13

Graph the inequality.
-$$y \geq \log ( x - 1 )$$

Accepted Answer

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

Question 14

Solve the system of equations.
-$$\begin{array} { l } 
x - y + 4 z = 3 \
4 x + z = 2 \
x + 4 y + z = 22
\end{array}$$

Accepted Answer

A)  $\{ ( 0,5,2 ) \}$ 
B)  $\{ ( 5,0,2 ) \}$ 
C)  $\{ ( 2,5,0 ) \}$ 
D)  $\{ ( 2,0,5 ) \}$ 
A)  $\{ ( 0,5,2 ) \}$ 
B)  $\{ ( 5,0,2 ) \}$ 
C)  $\{ ( 2,5,0 ) \}$ 
D)  $\{ ( 2,0,5 ) \}$

Question 15

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
-$$\frac { x } { 3 } + \frac { y } { 3 } = 2$$
$\mathrm { x } - \mathrm { y } = 4$

Accepted Answer

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

Question 16

Solve the problem.
-Steve invests in a circus production. The cost includes an overhead of $56,000, plus production costs of $5000 per performance. A sold-out performance brings in $13,000. Let x represent the number of sold-out
Performances and write the cost function, C and revenue function, R.

Accepted Answer

A)  $C ( x ) = 56,000 + 5000 x$
$R ( x ) = 13,000 x$ 
B)  $C ( x ) = 56,000 + 13,000 x$
$R ( x ) = 5000 x$ 
C)  $C ( x ) = 5000 x$
$R ( x ) = 56,000 + 13,000 x$ 
D)  $C ( x ) = 56,000 x + 5000$
$R ( x ) = 13,000 x$ 
A)  $C ( x ) = 56,000 + 5000 x$
$R ( x ) = 13,000 x$ 
B)  $C ( x ) = 56,000 + 13,000 x$
$R ( x ) = 5000 x$ 
C)  $C ( x ) = 5000 x$
$R ( x ) = 56,000 + 13,000 x$ 
D)  $C ( x ) = 56,000 x + 5000$
$R ( x ) = 13,000 x$

Question 17

Graph the inequality.
-$$- 2 x - 3 y \leq - 6$$

Accepted Answer

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

Question 18

Graph the inequality.
-$$\frac { x } { 5 } + \frac { y } { 3 } \leq 1$$

Accepted Answer

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

Question 19

Solve the problem.
-Steve invests in a circus production. The cost includes an overhead of $36,000, plus production costs of $6000 per performance. A sold-out performance brings in $9000. Determine the number of sold-out
Performances, x, needed to break even.

Accepted Answer

A) 12 performances 
B) 13 performances 
C) 14 performances 
D) 4 performances 
A) 12 performances 
B) 13 performances 
C) 14 performances 
D) 4 performances

Question 20

Graph the solution set of the system of inequalities or indicate that the system has no solution.
-$\begin{array}{l}
y>1 \
x \geq-1
\end{array}$

Accepted Answer

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

Graph the inequality. -x - y > -2

Solve the system of equations. - x-y+3z=-2 3x+z=0 x+3y+z=6

Graph the inequality. - $y \leq 6$ $Graph the inequality. - y \leq 6$

Graph the solution set of the system of inequalities or indicate that the system has no solution. - 2x+y>10 2x+y<-1 $Graph the solution set of the system of inequalities or indicate that the system has no solution. - \begin{array}{l} 2 x+y>10 \\ 2 x+y<-1 \end{array}$

Graph the solution set of the system of inequalities or indicate that the system has no solution. - 4x-y\leq-4 x+2y\geq4 $Graph the solution set of the system of inequalities or indicate that the system has no solution. - \begin{array}{l} 4 x-y \leq-4 \\ x+2 y \geq 4 \end{array}$

Solve the system by the addition method. - x+6y =11 4x+5y =-13

Solve the system of equations by the substitution method. - 6x+y=-7 3x-5y=-9

Graph the inequality. -x - y < -6

Graph the inequality. - $y \geq \log ( x - 1 )$ $Graph the inequality. - y \geq \log ( x - 1 )$

Solve the system of equations. - x-y+4z=3 4x+z=2 x+4y+z=22

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - $\frac { x } { 3 } + \frac { y } { 3 } = 2$ $\mathrm { x } - \mathrm { y } = 4$

Solve the problem. -Steve invests in a circus production. The cost includes an overhead of $56,000, plus production costs of $5000 per performance. A sold-out performance brings in $13,000. Let x represent the number of sold-out Performances and write the cost function, C and revenue function, R.

Graph the inequality. - $- 2 x - 3 y \leq - 6$ $Graph the inequality. - - 2 x - 3 y \leq - 6$

Graph the inequality. - $\frac { x } { 5 } + \frac { y } { 3 } \leq 1$ $Graph the inequality. - \frac { x } { 5 } + \frac { y } { 3 } \leq 1$

Solve the problem. -Steve invests in a circus production. The cost includes an overhead of $36,000, plus production costs of $6000 per performance. A sold-out performance brings in $9000. Determine the number of sold-out Performances, x, needed to break even.

Graph the solution set of the system of inequalities or indicate that the system has no solution. - y>1 x\geq-1 $Graph the solution set of the system of inequalities or indicate that the system has no solution. - \begin{array}{l} y>1 \\ x \geq-1 \end{array}$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants

Conic Sections

Sequences, Induction, and Probability

Filters

Exam 5: Systems of Equations and Inequalities

Graph the inequality. -x - y > -2

Solve the system of equations. - x-y+3z=-2 3x+z=0 x+3y+z=6

Graph the inequality. - y≤6y \leq 6y≤6

Graph the solution set of the system of inequalities or indicate that the system has no solution. - 2x+y>10 2x+y<-1

Graph the solution set of the system of inequalities or indicate that the system has no solution. - 4x-y\leq-4 x+2y\geq4

Graph the solution set of the system of inequalities or indicate that the system has no solution. - x\geq0 y\geq0 3x+3y\leq9 2x+y\leq4

Solve the system by the addition method. - x+6y =11 4x+5y =-13

Solve the system of equations by the substitution method. - 6x+y=-7 3x-5y=-9

Graph the inequality. -x - y < -6

Graph the inequality. - y≥log⁡(x−1)y \geq \log ( x - 1 )y≥log(x−1)

Solve the system of equations. - x-y+4z=3 4x+z=2 x+4y+z=22

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - x3+y3=2\frac { x } { 3 } + \frac { y } { 3 } = 23x​+3y​=2 x−y=4\mathrm { x } - \mathrm { y } = 4x−y=4

Solve the problem. -Steve invests in a circus production. The cost includes an overhead of $56,000, plus production costs of $5000 per performance. A sold-out performance brings in $13,000. Let x represent the number of sold-out Performances and write the cost function, C and revenue function, R.

Graph the inequality. - −2x−3y≤−6- 2 x - 3 y \leq - 6−2x−3y≤−6

Graph the inequality. - x5+y3≤1\frac { x } { 5 } + \frac { y } { 3 } \leq 15x​+3y​≤1

Solve the problem. -Steve invests in a circus production. The cost includes an overhead of $36,000, plus production costs of $6000 per performance. A sold-out performance brings in $9000. Determine the number of sold-out Performances, x, needed to break even.

Graph the solution set of the system of inequalities or indicate that the system has no solution. - y>1 x\geq-1

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants

Conic Sections

Sequences, Induction, and Probability

Filters

Graph the inequality. - $y \leq 6$ $Graph the inequality. - y \leq 6$

Graph the solution set of the system of inequalities or indicate that the system has no solution. - 2x+y>10 2x+y<-1 $Graph the solution set of the system of inequalities or indicate that the system has no solution. - \begin{array}{l} 2 x+y>10 \\ 2 x+y<-1 \end{array}$

Graph the solution set of the system of inequalities or indicate that the system has no solution. - 4x-y\leq-4 x+2y\geq4 $Graph the solution set of the system of inequalities or indicate that the system has no solution. - \begin{array}{l} 4 x-y \leq-4 \\ x+2 y \geq 4 \end{array}$

Graph the inequality. - $y \geq \log ( x - 1 )$ $Graph the inequality. - y \geq \log ( x - 1 )$

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - $\frac { x } { 3 } + \frac { y } { 3 } = 2$ $\mathrm { x } - \mathrm { y } = 4$

Graph the inequality. - $- 2 x - 3 y \leq - 6$ $Graph the inequality. - - 2 x - 3 y \leq - 6$

Graph the inequality. - $\frac { x } { 5 } + \frac { y } { 3 } \leq 1$ $Graph the inequality. - \frac { x } { 5 } + \frac { y } { 3 } \leq 1$

Graph the solution set of the system of inequalities or indicate that the system has no solution. - y>1 x\geq-1 $Graph the solution set of the system of inequalities or indicate that the system has no solution. - \begin{array}{l} y>1 \\ x \geq-1 \end{array}$