Question 1

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer.
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Accepted Answer

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

Question 2

Solve the system of equations using Cramerʹs Rule if it is applicable. If Cramerʹs Rule is not applicable, say so.
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Accepted Answer

A) x = 1, y = 6, z = 8; (1, 6, 8) 
B) x = 6, y = 8, z = 6; (6, 8, 6) 
C) x = 1, y = -6, z = -8; (1, -6, -8) 
D) x = 2, y = 4, z = 8; (2, 4, 8) 
A) x = 1, y = 6, z = 8; (1, 6, 8) 
B) x = 6, y = 8, z = 6; (6, 8, 6) 
C) x = 1, y = -6, z = -8; (1, -6, -8) 
D) x = 2, y = 4, z = 8; (2, 4, 8)

Question 3

Perform the indicated operation(s), whenever possible.
-Let   and   . Find A - B.

Accepted Answer

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

Question 4

Solve the system of equations using substitution.
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Accepted Answer

A) x = 1, y = 4; x = -3, y = 32 or (1, 4), (-3, 32) 
B) x = -1, y = 14; x = 3, y = 2 or (-1, 14), (3, 2) 
C) x = 1, y = 4; x = 0, y = 8 or (1, 4), (0, 8) 
D) x = -1, y = 14; x = 0, y = 8 or (-1, 14), (0, 8) 
A) x = 1, y = 4; x = -3, y = 32 or (1, 4), (-3, 32) 
B) x = -1, y = 14; x = 3, y = 2 or (-1, 14), (3, 2) 
C) x = 1, y = 4; x = 0, y = 8 or (1, 4), (0, 8) 
D) x = -1, y = 14; x = 0, y = 8 or (-1, 14), (0, 8)

Question 5

Set up the linear programming problem.
-Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 5 hours to makea hat and 3 hours to make an afghan, and she has no more than 54 hours available. She has material for nomore than 14 items, and she wants to make at least two afghans. Let x = the number of hats she makes andy = the number of afghans she makes. Write a system of inequalities that describes these constraints.

Accepted Answer

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

Question 6

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer.
-

Accepted Answer

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

Question 7

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is
consistent, give the solution.
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Accepted Answer

A) consistent; x = 1, y = 5, z = -5; (1, 5, -5) 
B) consistent; x = 1, y = -5, z = 5; (1, -5, 5) 
C) consistent; x = -5, y = 5, z = 1; (-5, 5, 1) 
D) inconsistent 
A) consistent; x = 1, y = 5, z = -5; (1, 5, -5) 
B) consistent; x = 1, y = -5, z = 5; (1, -5, 5) 
C) consistent; x = -5, y = 5, z = 1; (-5, 5, 1) 
D) inconsistent

Question 8

Graph the inequality.
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Accepted Answer

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

Question 9

Find the maximum or minimum value of the given objective function of a linear programming problem. The figure
illustrates the graph of feasible points.  
-z = 9x + 10y. Find minimum.

Accepted Answer

A) minimum: 56 
B) minimum: 57 
C) minimum: 68 
D) no minimum 
A) minimum: 56 
B) minimum: 57 
C) minimum: 68 
D) no minimum

Question 10

Perform the indicated operation(s), whenever possible.
-Let   and   Find A + B.

Accepted Answer

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

Question 11

Write the word or phrase that best completes each statement or answers the question.
-A store has a sale on workout gear. Mark bought three pairs of shorts and three T-shirts for $70.35 (beforetax). Later, he went back and bought two more pairs of shorts and four more T-shirts for $63.90 (beforetax). How much did the shorts and T-shirts cost?

Accepted Answer

shorts: $1

Question 12

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is
consistent, give the solution.
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Accepted Answer

A) consistent; x = 3, y = -1; (3, -1) 
B) consistent; x = -3, y = 1; (-3, 1) 
C) consistent; x = 3, y = -1, z = 10; (3, -1, 10) 
D) inconsistent 
A) consistent; x = 3, y = -1; (3, -1) 
B) consistent; x = -3, y = 1; (-3, 1) 
C) consistent; x = 3, y = -1, z = 10; (3, -1, 10) 
D) inconsistent

Question 13

Graph the inequality.
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Accepted Answer

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

Question 14

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer.
-

Accepted Answer

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

Question 15

Solve the system of equations by substitution.
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Accepted Answer

A) x = 3.5, y = -11.5; (3.5, -11.5) 
B) x = 3.5, y = 11.5; (3.5, 11.5) 
C) x = 8, y = -11.5; (8, -11.5) 
D) x = 8, y = 3.5; (8, 3.5) 
A) x = 3.5, y = -11.5; (3.5, -11.5) 
B) x = 3.5, y = 11.5; (3.5, 11.5) 
C) x = 8, y = -11.5; (8, -11.5) 
D) x = 8, y = 3.5; (8, 3.5)

Question 16

Write the word or phrase that best completes each statement or answers the question.
Graph the equations of the system. Then solve the system to find the points of intersection.
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Accepted Answer

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

Question 17

Solve the system of equations using substitution.
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Accepted Answer

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

Question 18

Write a system of linear inequalities that has the given graph.
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Accepted Answer

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

Question 19

Graph the system of inequalities.
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Accepted Answer

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

Question 20

Solve the system of equations. If the system has no solution, say that it is inconsistent.
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Accepted Answer

A)    where x is any real number or   , where x is any real number} 
B) x = -1,   
C) x = 0, y = 12; (0, 12) 
D) inconsistent 
A)    where x is any real number or   , where x is any real number} 
B) x = -1,   
C) x = 0, y = 12; (0, 12) 
D) inconsistent

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Solve the system of equations using Cramerʹs Rule if it is applicable. If Cramerʹs Rule is not applicable, say so. -

Perform the indicated operation(s), whenever possible. -Let and . Find A - B.

Solve the system of equations using substitution. -

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is consistent, give the solution. -

Graph the inequality. -

Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of feasible points. -z = 9x + 10y. Find minimum.

Perform the indicated operation(s), whenever possible. -Let and Find A + B.

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is consistent, give the solution. -

Graph the inequality. -

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Solve the system of equations by substitution. -

Write the word or phrase that best completes each statement or answers the question. Graph the equations of the system. Then solve the system to find the points of intersection. -

Solve the system of equations using substitution. -

Write a system of linear inequalities that has the given graph. -

Graph the system of inequalities. -

Solve the system of equations. If the system has no solution, say that it is inconsistent. -

Equations and Inequalities

Graphs

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Geometry

Sequences; Induction; the Binomial Theorem

Counting and Probability

Graphing Utilities

Filters

Exam 8: Systems of Equations and Inequalities

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Solve the system of equations using Cramerʹs Rule if it is applicable. If Cramerʹs Rule is not applicable, say so. -

Perform the indicated operation(s), whenever possible. -Let and . Find A - B.

Solve the system of equations using substitution. -

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is consistent, give the solution. -

Graph the inequality. -

Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of feasible points. -z = 9x + 10y. Find minimum.

Perform the indicated operation(s), whenever possible. -Let and Find A + B.

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is consistent, give the solution. -

Graph the inequality. -

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Solve the system of equations by substitution. -

Write the word or phrase that best completes each statement or answers the question. Graph the equations of the system. Then solve the system to find the points of intersection. -

Solve the system of equations using substitution. -

Write a system of linear inequalities that has the given graph. -

Graph the system of inequalities. -

Solve the system of equations. If the system has no solution, say that it is inconsistent. -

Equations and Inequalities

Graphs

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Geometry

Sequences; Induction; the Binomial Theorem

Counting and Probability

Graphing Utilities

Filters