Question 1

Use the substitution method to solve the system. If the equations of the system are dependent, or if the system is inconsistent, so indicate.

Accepted Answer

A)  (- 2, 3) 
B)  (0, 0) 
C)  (2, 3) 
D)    
E)  The system is inconsistent. 
A)  (- 2, 3) 
B)  (0, 0) 
C)  (2, 3) 
D)    
E)  The system is inconsistent. D

Question 2

Make a conjecture about the result of factoring a common factor from each element of a column in a determinant. Use your conjecture to help evaluate the determinant.

Accepted Answer

A)  88 
B)  72 
C)  84 
D)  76 
E)  80 
A)  88 
B)  72 
C)  84 
D)  76 
E)  80 E

Question 3

Use matrices to solve the system of equations. If the system has no solution, so indicate .

Accepted Answer

A)  ( 8, 7.5 ) 
B)  ( 7, 6.5 ) 
C)  ( 7, 7.5 ) 
D)  ( 8, 6.5 ) 
E)  No solution. 
A)  ( 8, 7.5 ) 
B)  ( 7, 6.5 ) 
C)  ( 7, 7.5 ) 
D)  ( 8, 6.5 ) 
E)  No solution. C

Question 4

A box contains $7.15 in nickels, dimes, and quarters. There are 44 coins in all, and the sum of the numbers of nickels and dimes is two less than the number of quarters. How many coins of each kind are there?

Accepted Answer

A)  17 nickels, 6 dimes, and 21 quarters 
B)  16 nickels, 5 dimes, and 23 quarters 
C)  16 nickels, 10 dimes, and 27 quarters 
D)  14 nickels, 7 dimes, and 23 quarters 
E)  18 nickels, 9 dimes, and 17 quarters 
A)  17 nickels, 6 dimes, and 21 quarters 
B)  16 nickels, 5 dimes, and 23 quarters 
C)  16 nickels, 10 dimes, and 27 quarters 
D)  14 nickels, 7 dimes, and 23 quarters 
E)  18 nickels, 9 dimes, and 17 quarters

Question 5

Which of the following ordered triples is a solution of the system   ?

Accepted Answer

A)  (- 9, -5,-9) 
B)  (-9, 5, 28) 
C)  (- 9,-18,-9) 
D)  (- 9,-5, 9) 
A)  (- 9, -5,-9) 
B)  (-9, 5, 28) 
C)  (- 9,-18,-9) 
D)  (- 9,-5, 9)

Question 6

Use matrices to solve the system of equations. If the system has no solution, so indicate.

Accepted Answer

A)    
B)    
C)    
D)    
E)  No solution. 
A)    
B)    
C)    
D)    
E)  No solution.

Question 7

Express the solution of the graphed system as a general ordered pair.

Accepted Answer

A)  ( x , y ) 
B)  ( x , x ) 
C)  ( x - y , 0) 
D)  (0, 0) 
A)  ( x , y ) 
B)  ( x , x ) 
C)  ( x - y , 0) 
D)  (0, 0)

Question 8

Solve the following system by the graphing method:   One of the equations is shown in the graph. Find values of x and y that satisfy the other equation and enter them in the table to graph the line. You may need to choose different values if you cannot determine the solution of the system with the points you have chosen. If you would like to use a value in the table that is not a whole number, enter it as a decimal number, not a fraction. Use the two lines to determine the solution of the system.   Hint : Remember to check that your solution satisfies both equations.

Accepted Answer

A)  ( 5, 6 ) 
B)  ( 4, 12 ) 
C)  ( 4, 7 ) 
D)  ( 4, 6 ) 
E)  none of the above 
A)  ( 5, 6 ) 
B)  ( 4, 12 ) 
C)  ( 4, 7 ) 
D)  ( 4, 6 ) 
E)  none of the above

Question 9

Use matrices to help find a general solution of the system of equations. Express your answer in terms of z .   Enter your answer as an ordered triple.

Accepted Answer

The answer of Use matrices to help find a general...

Question 10

Evaluate the determinant.

Accepted Answer

A)  -2 
B)  -50 
C)  -38 
D)  -26 
E)  -41 
A)  -2 
B)  -50 
C)  -38 
D)  -26 
E)  -41

Question 11

Part of $6,000 is invested at 9%, another part at 11%, and the remainder at 12% yearly interest. The total yearly income from the three investments is $650. The sum of the amounts invested at 9% and 11% equals the amount invested at 12%. How much is invested at each rate?

Accepted Answer

A)  $2,000 at 9%, $1,000 at 11%, and $3,000 at 12% 
B)  $1,500 at 9%, $0 at 11%, and $3,500 at 12% 
C)  $3,000 at 9%, $0 at 11%, and $3,000 at 12% 
D)  $1,500 at 9%, $1,000 at 11%, and $3,500 at 12% 
E)  $2,500 at 9%, $2,000 at 11%, and $2,000 at 12% 
A)  $2,000 at 9%, $1,000 at 11%, and $3,000 at 12% 
B)  $1,500 at 9%, $0 at 11%, and $3,500 at 12% 
C)  $3,000 at 9%, $0 at 11%, and $3,000 at 12% 
D)  $1,500 at 9%, $1,000 at 11%, and $3,500 at 12% 
E)  $2,500 at 9%, $2,000 at 11%, and $2,000 at 12%

Question 12

Use the substitution method to solve the system. If the equations of the system are dependent, or if the system is inconsistent, so indicate.

Accepted Answer

A)    
B)    
C)    
D)    
E)  The system is inconsistent. 
A)    
B)    
C)    
D)    
E)  The system is inconsistent.

Question 13

Solve the equation graphically. 5 x + 8 = 3

Accepted Answer

A)    x = -1 
B)    x = 3 
C)    x = -1 
D)    (-1, 3) 
A)    x = -1 
B)    x = 3 
C)    x = -1 
D)    (-1, 3)

Question 14

Solve the system of equations. If the system is inconsistent and thus unsolvable, so indicate; if the system is dependent and thus has infinite solutions, write your answer in terms of ordered triple.

Accepted Answer

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

Question 15

Solve the system.

Accepted Answer

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

Question 16

Solve the system.

Accepted Answer

A)    
B)    
C)    
D)  The system is inconsistent. 
E)  The system is dependent. 
A)    
B)    
C)    
D)  The system is inconsistent. 
E)  The system is dependent.

Question 17

Solve the system by graphing.

Accepted Answer

A)    ( x , -2.5 x + 0.5) 
B)    ( x , 2.5 x - 0.5) 
C)    (-2.5 x + 0.5, 2.5 x - 0.5) 
D)    (0, 0) 
A)    ( x , -2.5 x + 0.5) 
B)    ( x , 2.5 x - 0.5) 
C)    (-2.5 x + 0.5, 2.5 x - 0.5) 
D)    (0, 0)

Question 18

Use Cramer's rule to find the solution for the system.

Accepted Answer

The answer of Use Cramer's rule to find the solution...

Question 19

Solve the system by graphing.

Accepted Answer

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

Question 20

Use matrices to solve the system of equations. If the system has no solution, so indicate.

Accepted Answer

A)  ( 4, 4 ) 
B)  ( 4, 2 ) 
C)  ( 5, 2 ) 
D)  ( 5, 4 ) 
E)  No solution. 
A)  ( 4, 4 ) 
B)  ( 4, 2 ) 
C)  ( 5, 2 ) 
D)  ( 5, 4 ) 
E)  No solution.

Use the substitution method to solve the system. If the equations of the system are dependent, or if the system is inconsistent, so indicate.

Make a conjecture about the result of factoring a common factor from each element of a column in a determinant. Use your conjecture to help evaluate the determinant.

Use matrices to solve the system of equations. If the system has no solution, so indicate .

A box contains $7.15 in nickels, dimes, and quarters. There are 44 coins in all, and the sum of the numbers of nickels and dimes is two less than the number of quarters. How many coins of each kind are there?

Which of the following ordered triples is a solution of the system ?

Use matrices to solve the system of equations. If the system has no solution, so indicate.

Express the solution of the graphed system as a general ordered pair.

Use matrices to help find a general solution of the system of equations. Express your answer in terms of z . Enter your answer as an ordered triple.

Evaluate the determinant.

Part of $6,000 is invested at 9%, another part at 11%, and the remainder at 12% yearly interest. The total yearly income from the three investments is $650. The sum of the amounts invested at 9% and 11% equals the amount invested at 12%. How much is invested at each rate?

Use the substitution method to solve the system. If the equations of the system are dependent, or if the system is inconsistent, so indicate.

Solve the equation graphically. 5 x + 8 = 3

Solve the system of equations. If the system is inconsistent and thus unsolvable, so indicate; if the system is dependent and thus has infinite solutions, write your answer in terms of ordered triple.

Solve the system.

Solve the system.

Solve the system by graphing.

Use Cramer's rule to find the solution for the system.

Solve the system by graphing.

Use matrices to solve the system of equations. If the system has no solution, so indicate.

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Inequalities

Polynomials, Polynomial Functions, and Equations

Rational Expressions

Radical Expressions and Equations

Quadratic Equations and Functions; Inequalities; and Algebra, Composition, and Inverses of Functions

Exponential and Logarithmic Functions

Conic Sections and More Graphing

Miscellaneous Topics

Filters

Exam 3: Systems of Linear Equations

Use the substitution method to solve the system. If the equations of the system are dependent, or if the system is inconsistent, so indicate.

Make a conjecture about the result of factoring a common factor from each element of a column in a determinant. Use your conjecture to help evaluate the determinant.

Use matrices to solve the system of equations. If the system has no solution, so indicate .

A box contains $7.15 in nickels, dimes, and quarters. There are 44 coins in all, and the sum of the numbers of nickels and dimes is two less than the number of quarters. How many coins of each kind are there?

Which of the following ordered triples is a solution of the system ?

Use matrices to solve the system of equations. If the system has no solution, so indicate.

Express the solution of the graphed system as a general ordered pair.

Use matrices to help find a general solution of the system of equations. Express your answer in terms of z . Enter your answer as an ordered triple.

Evaluate the determinant.

Part of $6,000 is invested at 9%, another part at 11%, and the remainder at 12% yearly interest. The total yearly income from the three investments is $650. The sum of the amounts invested at 9% and 11% equals the amount invested at 12%. How much is invested at each rate?

Use the substitution method to solve the system. If the equations of the system are dependent, or if the system is inconsistent, so indicate.

Solve the equation graphically. 5 x + 8 = 3

Solve the system of equations. If the system is inconsistent and thus unsolvable, so indicate; if the system is dependent and thus has infinite solutions, write your answer in terms of ordered triple.

Solve the system.

Solve the system.

Solve the system by graphing.

Use Cramer's rule to find the solution for the system.

Solve the system by graphing.

Use matrices to solve the system of equations. If the system has no solution, so indicate.

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Inequalities

Polynomials, Polynomial Functions, and Equations

Rational Expressions

Radical Expressions and Equations

Quadratic Equations and Functions; Inequalities; and Algebra, Composition, and Inverses of Functions

Exponential and Logarithmic Functions

Conic Sections and More Graphing

Miscellaneous Topics

Filters