Question 1

Which of the following graphs correctly describes the system and its solution?     
A)
   
B)
   
C)
   
D)
None of these.

Accepted Answer

A

Question 2

Fred, Tiger, and Nancy play a round of golf together. Their combined score is 224. Fred's score was 4 more than Tiger's, and Nancy's score was 6 more than Fred's. What was each person's score?

Accepted Answer

A)  Fred = 74 ; Tiger = 70 ; Nancy = 80 
B)  Fred = 71 ; Tiger = 67 ; Nancy = 77 
C)  Fred = 76 ; Tiger = 72 ; Nancy = 82 
D)  Fred = 70 ; Tiger = 74 ; Nancy = 80 
A)  Fred = 74 ; Tiger = 70 ; Nancy = 80 
B)  Fred = 71 ; Tiger = 67 ; Nancy = 77 
C)  Fred = 76 ; Tiger = 72 ; Nancy = 82 
D)  Fred = 70 ; Tiger = 74 ; Nancy = 80 A

Question 3

Solve the system of equations.

Accepted Answer

A)  {(-1, 2, -2)} 
B)  {(-1, 0, 3)} 
C)  {(-4, 0, 3)} 
D)  {(0, 1, 1)} 
A)  {(-1, 2, -2)} 
B)  {(-1, 0, 3)} 
C)  {(-4, 0, 3)} 
D)  {(0, 1, 1)} B

Question 4

Solve the system of linear equations.

Accepted Answer

A)  No solution. The system is inconsistent. 
B)  {(1, 5)} 
C)  {(3, 7)} 
D)  {(-3, -6)} 
A)  No solution. The system is inconsistent. 
B)  {(1, 5)} 
C)  {(3, 7)} 
D)  {(-3, -6)}

Question 5

Suzanne invested $18,100 in two mutual fund accounts: the Abernathy Fund and the Brice Fund. During the subsequent year, The Abernathy Fund earned 11% and the Brice account earned 6%. At the end of the year, the total interest earned was $1,391. How much did Suzanne invest in each fund?

Accepted Answer

A)  $6,600 in the Abernathy Fund, $11,500 in the Brice Fund 
B)  $5,100 in the Abernathy Fund, $13,000 in the Brice Fund 
C)  $6,100 in the Abernathy Fund, $12,000 in the Brice Fund 
D)  $6,600 in the Abernathy Fund, $11,700 in the Brice Fund 
A)  $6,600 in the Abernathy Fund, $11,500 in the Brice Fund 
B)  $5,100 in the Abernathy Fund, $13,000 in the Brice Fund 
C)  $6,100 in the Abernathy Fund, $12,000 in the Brice Fund 
D)  $6,600 in the Abernathy Fund, $11,700 in the Brice Fund

Question 6

Solve the system of equations. 0.5x + 2y = 1.25
-0)875x + 1.5y = 2.8125

Accepted Answer

A)  {(-1, 1.5)} 
B)  {(0, 1)} 
C)  {(0, 3)} 
D)  {(-1.5, 1)} 
A)  {(-1, 1.5)} 
B)  {(0, 1)} 
C)  {(0, 3)} 
D)  {(-1.5, 1)}

Question 7

When three linear equations (each in three variables) are graphed, two of the equations are seen to be parallel planes. The system is

Accepted Answer

A)  normal. 
B)  incomplete. 
C)  inconsistent. 
D)  dependent. 
A)  normal. 
B)  incomplete. 
C)  inconsistent. 
D)  dependent.

Question 8

When the graphs of two independent linear equations (each in three variables) intersect, the intersection is

Accepted Answer

A)  a line. 
B)  a plane. 
C)  a point. 
D)  None of these. 
A)  a line. 
B)  a plane. 
C)  a point. 
D)  None of these.

Question 9

Solve the system of linear equations by the substitution method. 8x = -3y - 15
5x - 8y = 40

Accepted Answer

A)  {(-2, -4)} 
B)  {(0, -5)} 
C)  No solution. The system is inconsistent. 
D)  {(2, -2)} 
A)  {(-2, -4)} 
B)  {(0, -5)} 
C)  No solution. The system is inconsistent. 
D)  {(2, -2)}

Question 10

When rolling a pair of dice, the probability of getting a particular total is not very high. For example, the probability of failing to roll a total of 7 is 5 times the probability of successfully rolling a total of 7. The total probability (probability of failing to roll a 7 + probability of successfully rolling a 7) is 1. What is the probability of rolling a 7?

Accepted Answer

A)  1 in 6 
B)  1 in 18 
C)  1 in 9 
D)  None of these. 
A)  1 in 6 
B)  1 in 18 
C)  1 in 9 
D)  None of these.

Question 11

Solve the system of equations. -3x + 3y - 4z = -58
5x + 2y - z = 1
-4x - 3y + 3z = 23

Accepted Answer

A)  {(4, -4, 2)} 
B)  {(1, -6, 7)} 
C)  {(4, -6, 7)} 
D)  {(-6, 6, 5)} 
A)  {(4, -4, 2)} 
B)  {(1, -6, 7)} 
C)  {(4, -6, 7)} 
D)  {(-6, 6, 5)}

Question 12

Cashews sell for $5 per pound and peanuts sell for $2 per pound. How many pounds of each would you use to make 20 pounds of a mixture that sells for $4.25 per pound?

Accepted Answer

A)  13 lb cashews, 7 lb peanuts 
B)  16 lb cashews, 4 lb peanuts 
C)  17 lb cashews, 3 lb peanuts 
D)  15 lb cashews, 5 lb peanuts 
A)  13 lb cashews, 7 lb peanuts 
B)  16 lb cashews, 4 lb peanuts 
C)  17 lb cashews, 3 lb peanuts 
D)  15 lb cashews, 5 lb peanuts

Question 13

Solve the system of equations. 2x - 3y + z = 4
8x - 12y + 4z = 16
-4x + 6y - 2z = -8

Accepted Answer

A)  {(-3, 6, 7)} 
B)  {(-4, -2, -1)} 
C)  {F1F1F1S1F1F1F10} 
D)  {(x, y, z) | 2x - 3y + z = 4} 
A)  {(-3, 6, 7)} 
B)  {(-4, -2, -1)} 
C)  {F1F1F1S1F1F1F10} 
D)  {(x, y, z) | 2x - 3y + z = 4}

Question 14

Solve the system of equations. -x + y - z = 8
4x - 2y + 5z = -28
2x - 2y + 2z = -14

Accepted Answer

A)  {(0, 4, -4)} 
B)  {F1F1F1S1F1F1F10} 
C)  {(x, y, z) | -x + y - z = 8} 
D)  {(x, y, z) | 4x - 2y + 5z = -28} 
A)  {(0, 4, -4)} 
B)  {F1F1F1S1F1F1F10} 
C)  {(x, y, z) | -x + y - z = 8} 
D)  {(x, y, z) | 4x - 2y + 5z = -28}

Question 15

For Monday morning's staff meeting, Jim bought 2 bags of bagels and 3 packages of cream cheese and paid $11.50 (excluding sales tax). For Friday's meeting, he bought 4 bags of bagels and 2 packages of cream cheese and paid $13.00 (again, excluding sales tax). How much do bags of bagels and packages of cream cheese cost?

Accepted Answer

A)  $1.75 per bag for bagels, $2.75 per package for cream cheese 
B)  $3.25 per bag for bagels, $2.50 per package for cream cheese 
C)  $2.00 per bag for bagels, $2.50 per package for cream cheese 
D)  $2.50 per bag for bagels, $2.00 per package for cream cheese 
A)  $1.75 per bag for bagels, $2.75 per package for cream cheese 
B)  $3.25 per bag for bagels, $2.50 per package for cream cheese 
C)  $2.00 per bag for bagels, $2.50 per package for cream cheese 
D)  $2.50 per bag for bagels, $2.00 per package for cream cheese

Question 16

For the system find the value of a so that the solution set to the system is {(7, 3)}.

Accepted Answer

A)    
B)  3 
C)  10 
D)  -3 
A)    
B)  3 
C)  10 
D)  -3

Question 17

Solve the system of linear equations by the substitution method.

Accepted Answer

A) 
  
B) 
  
C)  No solution. The system is inconsistent. 
D) 
  
A) 
  
B) 
  
C)  No solution. The system is inconsistent. 
D)

Exam 7: Section 1: Systems of Linear Equations

Which of the following graphs correctly describes the system and its solution? A) B) C) D) None of these.

Fred, Tiger, and Nancy play a round of golf together. Their combined score is 224. Fred's score was 4 more than Tiger's, and Nancy's score was 6 more than Fred's. What was each person's score?

Solve the system of equations.

Solve the system of linear equations.

Suzanne invested $18,100 in two mutual fund accounts: the Abernathy Fund and the Brice Fund. During the subsequent year, The Abernathy Fund earned 11% and the Brice account earned 6%. At the end of the year, the total interest earned was $1,391. How much did Suzanne invest in each fund?

Solve the system of equations. 0.5x + 2y = 1.25 -0)875x + 1.5y = 2.8125

When three linear equations (each in three variables) are graphed, two of the equations are seen to be parallel planes. The system is

When the graphs of two independent linear equations (each in three variables) intersect, the intersection is

Solve the system of linear equations by the substitution method. 8x = -3y - 15 5x - 8y = 40

Solve the system of equations. -3x + 3y - 4z = -58 5x + 2y - z = 1 -4x - 3y + 3z = 23

Cashews sell for $5 per pound and peanuts sell for $2 per pound. How many pounds of each would you use to make 20 pounds of a mixture that sells for $4.25 per pound?

Solve the system of equations. 2x - 3y + z = 4 8x - 12y + 4z = 16 -4x + 6y - 2z = -8

Solve the system of equations. -x + y - z = 8 4x - 2y + 5z = -28 2x - 2y + 2z = -14

For the system find the value of a so that the solution set to the system is {(7, 3)}.

Solve the system of linear equations by the substitution method.

Section 1: Real Numbers and Their Properties

Section 2: Real Numbers and Their Properties

Section 1: Linear Equations and Inequalities in One Variable

Section 2: Linear Equations and Inequalities in One Variable

Section 1: Linear Equations and Inequalities in Two Variables

Section 2: Linear Equations and Inequalities in Two Variables

Section 1: Exponents and Polynomials

Section 2: Exponents and Polynomials

Section 1: Factoring

Section 2: Factoring

Section 1: Rational Expressions

Section 2: Rational Expressions

Section 2: Systems of Linear Equations

Section 1: More on Inequalities

Section 2: More on Inequalities

Section 1: Radicals and Rational Exponents

Section 2: Radicals and Rational Exponents

Section 1: Quadratic Equations and Inequalities

Section 2: Quadratic Equations and Inequalities

Section 1: Functions

Section 2: Functions

Section 1: Exponential and Logarithmic Functions

Section 2: Exponential and Logarithmic Functions

Section 1: Nonlinear Systems and the Conic Sections

Section 2: Nonlinear Systems and the Conic Sections

Section 1: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Section 2: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Mathematical Problem Set

Algebraic Equations and Problem Solving

Algebra and Math Problems

Algebraic Equation Practice

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