Question 1

Graph the system of inequalities.
-$\begin{array}{c}
x+2 y \geq 2 \
x-y \leq 0
\end{array}$

Accepted Answer

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

Question 2

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered
triple involving variable z.
-$$\begin{array} { l } 
x + y + z = 7 \
x - y + 2 z = 7
\end{array}$$

Accepted Answer

A)  $( 8 , - 3,2 )$ 
B)  $( - 3 z + 14,2 z - 7 , z )$ 
C)  $( 4,1,2 )$ 
D)  $\left( - \frac { 3 } { 2 } z + 7 , \frac { 1 } { 2 } z , z \right)$ 
A)  $( 8 , - 3,2 )$ 
B)  $( - 3 z + 14,2 z - 7 , z )$ 
C)  $( 4,1,2 )$ 
D)  $\left( - \frac { 3 } { 2 } z + 7 , \frac { 1 } { 2 } z , z \right)$

Question 3

Graph the system of inequalities.
-$\begin{array}{l}
x^{2}+y^{2} \leq 64 \
x+y>1
\end{array}$

Accepted Answer

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

Question 4

Solve the problem.
-The area of a rectangular piece of cardboard shown is 688 square inches. The cardboard is used to make an open box by cutting a 4-inch square from each corner and turning up the sides. If the box is to have a volume of 1120 cubic inches, find the dimensions of the cardboard that must be used.

Accepted Answer

A) 16 inches by 43 inches 
B) 8 inches by 31 inches 
C) 12 inches by 39 inches 
D) 20 inches by 47 inches 
A) 16 inches by 43 inches 
B) 8 inches by 31 inches 
C) 12 inches by 39 inches 
D) 20 inches by 47 inches

Question 5

Solve the system of equations by substitution.
-9x + y = 0 -9x + y = -18

Accepted Answer

A) (-1, 9) 
B) (1, -9) 
C) (-1, -9) 
D) (1, 18) 
A) (-1, 9) 
B) (1, -9) 
C) (-1, -9) 
D) (1, 18)

Question 6

Solve the system of equations by substitution.
-x + y = -7 x - y = 16

Accepted Answer

A) (4.5, 11.5) 
B) (4.5, -11.5) 
C) (7, -11.5) 
D) (7, 4.5) 
A) (4.5, 11.5) 
B) (4.5, -11.5) 
C) (7, -11.5) 
D) (7, 4.5)

Question 7

A system of nonlinear equations is given. Sketch the graph of the equation of the system and then determine the number of real solutions to the system. Do not solve the system.
-$$\begin{array} { l } 
2 x ^ { 2 } = y + 5 \
y = - 10 x + 7
\end{array}$$

Accepted Answer

A) $\text { Two }$
  
B) $\text { One }$
  
C)  One
  
D)  Two
  
A) $\text { Two }$
  
B) $\text { One }$
  
C)  One
  
D)  Two

Question 8

Graph the system of inequalities.
-$\begin{array}{c}
2 x+3 y \leq 6 \
x-y \leq 3 \
x \geq 1
\end{array}$

Accepted Answer

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

Question 9

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } - 3 y ^ { 2 } = 1 \
2 x ^ { 2 } + 3 y ^ { 2 } = 47
\end{array}$$

Accepted Answer

A)  $( 4,5 ) , ( - 4 , - 5 )$ 
B)  $( 5,4 ) , ( - 5 , - 4 )$ 
C)  $( 4,5 ) , ( - 4,5 ) , ( 4 , - 5 ) , ( - 4 , - 5 )$ 
D)  $( 5,4 ) , ( - 5,4 ) , ( 5 , - 4 ) , ( - 5 , - 4 )$ 
A)  $( 4,5 ) , ( - 4 , - 5 )$ 
B)  $( 5,4 ) , ( - 5 , - 4 )$ 
C)  $( 4,5 ) , ( - 4,5 ) , ( 4 , - 5 ) , ( - 4 , - 5 )$ 
D)  $( 5,4 ) , ( - 5,4 ) , ( 5 , - 4 ) , ( - 5 , - 4 )$

Question 10

Graph the inequality.
-

Accepted Answer

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

Question 11

Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers.
-The sum of two numbers is -6 and their product is -216. Find the numbers.

Accepted Answer

A) 12 and -18; -12 and 18 
B) 12 and 18; -12 and -18 
C) -12 and 18 
D) 12 and -18 
A) 12 and -18; -12 and 18 
B) 12 and 18; -12 and -18 
C) -12 and 18 
D) 12 and -18

Question 12

Determine if the ordered pair is a solution to the system of linear inequalities in two variables.
-$$\begin{array} { l } 
2 x + 5 y  14 \
x < 1 \
y \geq - 4
\end{array}$$
$( 1 , - 4 )$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 13

Write the partial fraction decomposition of the rational expression.
-$$\frac { 14 x - 54 } { ( x - 1 ) ( x - 9 ) }$$

Accepted Answer

A)  $\frac { 4 } { x - 1 } + \frac { 10 } { x - 9 }$ 
B)  $\frac { 5 } { x - 1 } + \frac { - 9 } { x - 9 }$ 
C)  $\frac { 13 } { x - 1 } + \frac { 1 } { x - 9 }$ 
D)  $\frac { 5 } { x - 1 } + \frac { 9 } { x - 9 }$ 
A)  $\frac { 4 } { x - 1 } + \frac { 10 } { x - 9 }$ 
B)  $\frac { 5 } { x - 1 } + \frac { - 9 } { x - 9 }$ 
C)  $\frac { 13 } { x - 1 } + \frac { 1 } { x - 9 }$ 
D)  $\frac { 5 } { x - 1 } + \frac { 9 } { x - 9 }$

Question 14

Solve the problem.
-The Family Arts Center charges $23 for adults, $16 for senior citizens, and $6 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $12,492 for 862 tickets sold. There were 40 more children than adults. How many children attended?

Accepted Answer

A) 300 children 
B) 451 children 
C) 330 children 
D) 222 children 
A) 300 children 
B) 451 children 
C) 330 children 
D) 222 children

Question 15

Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { l } 
( 1,2,3 ) \
5 x + 5 y + z = 18 \
4 x - 2 y - z = - 3 \
4 x + y + 3 z = 15
\end{array}$$

Accepted Answer

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

Question 16

Graph the system of inequalities.
-$\begin{array}{l}
-x+2 y \leq-6 \
3 x+2 y>-18
\end{array}$

Accepted Answer

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

Question 17

Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers.
-The difference between the squares of two numbers is 80. Twice the square of the second number subtracted from the square of the first number is 16. Find the numbers.

Accepted Answer

A) 12 and 8 
B) 12 and 8; -12 and 8; 12 and -8; -12 and -8 
C) 12 and 8; -12 and -8 
D) 12 and 8; -12 and 8; 12 and -8 
A) 12 and 8 
B) 12 and 8; -12 and 8; 12 and -8; -12 and -8 
C) 12 and 8; -12 and -8 
D) 12 and 8; -12 and 8; 12 and -8

Question 18

Determine if the ordered pair is a solution to the given inequality.
-$$4 x + 5 y \leq 8 ; \left( \frac { 7 } { 4 } , \frac { 3 } { 5 } \right)$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 19

Solve the system of equations by substitution.
-$$\begin{array} { l } 
\frac { 1 } { 2 } x + \frac { 2 } { 3 } y = 32 \
\frac { 1 } { 4 } x - \frac { 5 } { 9 } y = 40
\end{array}$$

Accepted Answer

A) (100, 27) 
B) (-100, -27) 
C) (100, -27) 
D) (-100, 27) 
A) (100, 27) 
B) (-100, -27) 
C) (100, -27) 
D) (-100, 27)

Question 20

Solve the problem.
-A basketball player scored 24 points in a game. The number of three-point field goals the player made was 14 less than three times the number of free throws (each worth 1 point). Twice the number of two-point field goals the player made was 15 more than the number of three-point field goals made. Find the number of free-throws, two-point field goals, and three-point field goals that the player made in the game.

Accepted Answer

A) 5 free throws; 8 two-point field goals; 1 three-point field goals 
B) 5 free throws; 9 two-point field goals; 3 three-point field goals 
C) 6 free throws; 8 two-point field goals; 4 three-point field goals 
D) 5 free throws; 1 two-point field goals; 8 three-point field goals 
A) 5 free throws; 8 two-point field goals; 1 three-point field goals 
B) 5 free throws; 9 two-point field goals; 3 three-point field goals 
C) 6 free throws; 8 two-point field goals; 4 three-point field goals 
D) 5 free throws; 1 two-point field goals; 8 three-point field goals

Graph the system of inequalities. - x+2y\geq2 x-y\leq0 $Graph the system of inequalities. - \begin{array}{c} x+2 y \geq 2 \\ x-y \leq 0 \end{array}$

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z. - x+y+z=7 x-y+2z=7

Graph the system of inequalities. - +\leq64 x+y>1 $Graph the system of inequalities. - \begin{array}{l} x^{2}+y^{2} \leq 64 \\ x+y>1 \end{array}$

Solve the system of equations by substitution. -9x + y = 0 -9x + y = -18

Solve the system of equations by substitution. -x + y = -7 x - y = 16

Graph the system of inequalities. - 2x+3y\leq6 x-y\leq3 x\geq1 $Graph the system of inequalities. - \begin{array}{c} 2 x+3 y \leq 6 \\ x-y \leq 3 \\ x \geq 1 \end{array}$

Determine the real solutions to the system of nonlinear equations. - -3=1 2+3=47

Graph the inequality. -

Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers. -The sum of two numbers is -6 and their product is -216. Find the numbers.

Determine if the ordered pair is a solution to the system of linear inequalities in two variables. - 2x+5y<14 -5x+2y>14 x<1 y\geq-4 $( 1 , - 4 )$

Write the partial fraction decomposition of the rational expression. - $\frac { 14 x - 54 } { ( x - 1 ) ( x - 9 ) }$

Determine if the given ordered triple is a solution of the system. - (1,2,3) 5x+5y+z=18 4x-2y-z=-3 4x+y+3z=15

Graph the system of inequalities. - -x+2y\leq-6 3x+2y>-18 $Graph the system of inequalities. - \begin{array}{l} -x+2 y \leq-6 \\ 3 x+2 y>-18 \end{array}$

Determine if the ordered pair is a solution to the given inequality. - $4 x + 5 y \leq 8 ; \left( \frac { 7 } { 4 } , \frac { 3 } { 5 } \right)$

Solve the system of equations by substitution. - x+y=32 x-y=40

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 7: Systems of Equations and Inequalities

Graph the system of inequalities. - x+2y\geq2 x-y\leq0

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z. - x+y+z=7 x-y+2z=7

Graph the system of inequalities. - +\leq64 x+y>1

Solve the system of equations by substitution. -9x + y = 0 -9x + y = -18

Solve the system of equations by substitution. -x + y = -7 x - y = 16

A system of nonlinear equations is given. Sketch the graph of the equation of the system and then determine the number of real solutions to the system. Do not solve the system. - 2=y+5 y=-10x+7

Graph the system of inequalities. - 2x+3y\leq6 x-y\leq3 x\geq1

Determine the real solutions to the system of nonlinear equations. - -3=1 2+3=47

Graph the inequality. -

Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers. -The sum of two numbers is -6 and their product is -216. Find the numbers.

Determine if the ordered pair is a solution to the system of linear inequalities in two variables. - 2x+5y<14 -5x+2y>14 x<1 y\geq-4 (1,−4)( 1 , - 4 )(1,−4)

Write the partial fraction decomposition of the rational expression. - 14x−54(x−1)(x−9)\frac { 14 x - 54 } { ( x - 1 ) ( x - 9 ) }(x−1)(x−9)14x−54​

Determine if the given ordered triple is a solution of the system. - (1,2,3) 5x+5y+z=18 4x-2y-z=-3 4x+y+3z=15

Graph the system of inequalities. - -x+2y\leq-6 3x+2y>-18

Determine if the ordered pair is a solution to the given inequality. - 4x+5y≤8;(74,35)4 x + 5 y \leq 8 ; \left( \frac { 7 } { 4 } , \frac { 3 } { 5 } \right)4x+5y≤8;(47​,53​)

Solve the system of equations by substitution. - x+y=32 x-y=40

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Graph the system of inequalities. - x+2y\geq2 x-y\leq0 $Graph the system of inequalities. - \begin{array}{c} x+2 y \geq 2 \\ x-y \leq 0 \end{array}$

Graph the system of inequalities. - +\leq64 x+y>1 $Graph the system of inequalities. - \begin{array}{l} x^{2}+y^{2} \leq 64 \\ x+y>1 \end{array}$

Graph the system of inequalities. - 2x+3y\leq6 x-y\leq3 x\geq1 $Graph the system of inequalities. - \begin{array}{c} 2 x+3 y \leq 6 \\ x-y \leq 3 \\ x \geq 1 \end{array}$

Determine if the ordered pair is a solution to the system of linear inequalities in two variables. - 2x+5y<14 -5x+2y>14 x<1 y\geq-4 $( 1 , - 4 )$

Write the partial fraction decomposition of the rational expression. - $\frac { 14 x - 54 } { ( x - 1 ) ( x - 9 ) }$

Graph the system of inequalities. - -x+2y\leq-6 3x+2y>-18 $Graph the system of inequalities. - \begin{array}{l} -x+2 y \leq-6 \\ 3 x+2 y>-18 \end{array}$

Determine if the ordered pair is a solution to the given inequality. - $4 x + 5 y \leq 8 ; \left( \frac { 7 } { 4 } , \frac { 3 } { 5 } \right)$