Deck 8: Systems of Equations and Inequalities

Question 1

The length of a rectangle is 9 in. more than twice its width. If the perimeter of the rectangle is 54 in., find the width of the rectangle.

A) 5 in.
B) 6 in.
C) 7 in.
D) 8 in.

Answer 1

6 in.

Question 2

Solve using any method and identify the system as consistent, inconsistent, or dependent.

Answer 2

{(x, y) | 5x + 0 = 4y}; consistent/dependent

Question 3

Solve using any method and identify the system as consistent, inconsistent, or dependent.

Answer 3

Ø; inconsistent

Question 4

Adult tickets for a play cost $9 and child tickets cost $1. If there were 22 people at a performance and the theatre collected $182 from ticket sales, how many children attended the play?

A) 1 child
B) 2 children
C) 3 children
D) 20 children

Question 5

Substitute the x- and y-values indicated by the ordered pair (-3, -2) to determine if it solves the system.

A) Yes
B) No

Question 6

Solve using any method and identify the system as consistent, inconsistent, or dependent.

Question 7

Solve the system using substitution. Write your answer as an ordered pair.

A) (9, -3)
B) (8, -3)
C) (9, -2)
D) (8, -2)

Question 8

Solve the system by graphing. If the solution does not appear to be a lattice point, estimate the solution to the nearest tenth (indicate that your solution is an estimate)

Question 9

Solve the system using substitution. Write your answer as an ordered pair.

Question 10

Solve the system by graphing. If the solution does not appear to be a lattice point, estimate the solution to the nearest tenth (indicate that your solution is an estimate).

Question 11

Solve the system by elimination.

A) (8, -8)
B) (9, -7)
C) (8, -7)
D) (9, -8)

Question 12

Identify the equation and variable that makes the substitution method easiest to use. Then solve the system.

Question 13

Solve the system by elimination. The system must first be written in standard form.

Question 14

Solve using any method and identify the system as consistent, inconsistent, or dependent.

A) (-1, 3); consistent/independent
B) (-1, 3); consistent/dependent
C) {(-1, 3) | 2x + y = 1}; consistent/dependent
D) Ø; inconsistent

Question 15

Solve the system by graphing. If the solution does not appear to be a lattice point, estimate the solution to the nearest tenth (indicate that your solution is an estimate).

Question 16

Whitney invested $8,000, part at 14% and part at 8%. If the total interest at the end of the year is $940, how much did she invest at each rate?

Question 17

Substitute the x- and y-values indicated by the ordered pair (9, -5) to determine if it solves the system.

A) Yes
B) No

Question 18

Solve the system by graphing. If the solution does not appear to be a lattice point, estimate the solution to the nearest tenth (indicate that your solution is an estimate).

Question 19

Solve the system by graphing. If the solution does not appear to be a lattice point, estimate the solution to the nearest tenth (indicate that your solution is an estimate).

Question 20

Find any four ordered triples that satisfy the equation.
x - y + z = -3

Question 21

Solve the linear inequality by shading the appropriate half plane.
-3x + y $\ge$ 0

Question 22

Solve using the elimination method. If the system is inconsistent or dependent, so state. For a system with linear dependence, write the answer in terms of a parameter. For coincident dependence, state the solution in set notation.

A) (-2, -1, 3)
B) (-z + 1, -z + 2, z)
C)
D) no solution, inconsistent

Question 23

Determine if the ordered triple (2, -1, 1) is a solution of the system.

A) Yes
B) No

Question 24

A coin jar contains nickels, dimes, and quarters. There are 38 coins in all. There are 2 more nickels than quarters. The value of the dimes is $2.70 less than the value of the quarters. How many coins of each type are in the jar?

Question 25

Solve the system using the elimination method. If the system is inconsistent or dependent, so state.

A) (4, -2, -5)
B) (4, -3, -4)
C) dependent
D) no solution, inconsistent

Question 26

Determine whether the ordered pair (0, 0) is a solution. 10x - 3y > 5

A) Yes
B) No

Question 27

Solve the system using elimination and back-substitution.

Question 28

Solve the linear inequality by shading the appropriate half plane.
x - y $\le$ 2

Question 29

Decompose the rational expression into partial fractions.

Question 30

Solve using the elimination method. If the system is inconsistent or dependent, so state. For a system with linear dependence, write the answer in terms of a parameter. For coincident dependence, state the solution in set notation.

Question 31

Solve the system using the elimination method.

A) (4, 0, 4)
B) (3, 1, 4)
C) (3, 1, 3)
D) (4, 0, 3)

Question 32

Solve the system using the elimination method. If the system is inconsistent or dependent, so state. For systems with linear dependence, write the answer as an ordered triple in terms of a parameter.

Question 33

Solve the system using the elimination method. If the system has coincident dependence, state the solution in set notation.

Question 34

Solve the linear inequality by shading the appropriate half plane.
2x + 3y > 6

Question 35

Decompose the rational expression into partial fractions.

A)
B)
C)
D)

Question 36

Solve the linear inequality by shading the appropriate half plane.
3x + y $\le$ 5

Question 37

Decompose the rational expression into partial fractions.

Question 38

Determine if the ordered triple (0, -2, 1) is a solution of the system.

A) Yes
B) No

Question 39

Solve the system using elimination. If the system is linearly dependent, state the general solution in terms of a parameter.

A) (-1, -7, 0)
B) (3, 3, 2)
C) (2z - 3, 5z - 7, z)
D) no solution, inconsistent

Question 40

Solve using the elimination method. If the system is inconsistent or dependent, so state. For a system with linear dependence, write the answer in terms of a parameter. For coincident dependence, state the solution in set notation.

Question 41

Solve the system of inequalities by graphing the solution region.

A)
(Tickmarks are spaced one unit apart.)
B)
(Tickmarks are spaced one unit apart.)
C)
(Tickmarks are spaced one unit apart.)
D)
(Tickmarks are spaced one unit apart.)

Question 42

Determine the size of the matrix and identify the entry located in the second row and first column.

A) 3 * 2; 8
B) 2 * 3; 8
C) 3 * 2; 4.1
D) 2 * 3; 4.1

Question 43

Solve the system of inequalities by graphing the solution region.

Question 44

Solve the system of inequalities by graphing the solution region.

Question 45

Write the system of equations for the matrix. Then use back-substitution to find its solution.

Question 46

Determine whether the ordered pairs given are solutions to the system. (0, 0), (3, -1), (-3, -3), and (-5, 1)

Question 47

Solve the system of inequalities by graphing the solution region.

A)
(Tickmarks are spaced one unit apart.)
B)
(Tickmarks are spaced one unit apart.)
C)
(Tickmarks are spaced one unit apart.)
D)
(Tickmarks are spaced one unit apart.)

Question 48

Determine the size of the matrix and identify the entry located in the second row and first column.

A) 3 * 2; 6
B) 2 * 3; 6
C) 3 * 2; 1.3
D) 2 * 3; 1.3

Question 49

Solve the system of inequalities by graphing the solution region.

Question 50

Perform the indicated row operation, then write the new matrix. -2R1 + R2 → R2

Question 51

Use the following to answer questions :
Use back-substitution to find the solution.

A) (27, -7, -5)
B) (-5, -7, 27)
C) (25, -7, -5)
D) (-5, -7, 25)

Question 52

Form the augmented matrix, then name the diagonal entries of the coefficient matrix.

Question 53

Solve the system of inequalities by graphing the solution region.

Question 54

Solve the system of inequalities by graphing the solution region.

Question 55

A stationary store sells rolls of standard gift wrap and deluxe gift wrap. They can stock a total of 110 rolls of gift wrap, of which at least 40 must be standard wrap and at least 20 must be deluxe wrap. The profit on a roll of standard wrap is $4 and the profit on a roll of deluxe wrap is $5. How many rolls of each type of gift wrap should the store stock to maximize their profit?

Question 56

Use the following to answer questions :
Esther wants to spend no more than $60 buying gifts for her friends Barb and Wanda. She wants to spend at least $20 on Wanda's gift.
Solve the system of linear inequalities.

A)

B)

C)

D)

Question 57

Use the following to answer questions :
Write the system of equations corresponding to the matrix.

Question 58

Use the following to answer questions :
Esther wants to spend no more than $60 buying gifts for her friends Barb and Wanda. She wants to spend at least $20 on Wanda's gift.
Let B represent the amount Esther spends on Barb's gift and W represent the amount she spends on Wanda's gift. Write a system of linear inequalities that models the information.

A)
B)
C)
D)

Question 59

Determine which of the ordered pairs given produces the maximum value of P(x, y). P(x, y) = 20x + 50y; (0, 0), (5, 2), (4, 0), (0, 6)

A) (0, 0)
B) (5, 2)
C) (4, 0)
D) (0, 6)

Question 60

Form the augmented matrix, then name the diagonal entries of the coefficient matrix.

A)

Diagonal entries 6, -7, 2
B)

Diagonal entries 6, -7, -2
C)

Diagonal entries 6, -7, -2
D)

Diagonal entries 6, -7, 2

Question 61

Perform the indicated operation, if possible. Do not use a calculator. AB

A)

B)

C)

D) matrix multiplication not possible

Question 62

Perform the indicated operation, if possible. Do not use a calculator. If the operation cannot be completed, state why. A²

Question 63

Perform the indicated operation, if possible. Do not use a calculator. A²

A)

B)

C)

D) matrix multiplication not possible

Question 64

Perform the indicated operation, if possible. Do not use a calculator. If the operation cannot be completed, state why. AB

Question 65

Solve the system by triangularizing the augmented matrix and using back substitution. If the system is linearly dependent, give the solution in terms of a parameter.

A) (2, 1, 3)
B) (2, 1, 2)
C) coincident dependence; {(x, y, z) | x + y - 3z = -6}
D) no solution, inconsistent

Question 66

Find the inverse of the 2 * 2 matrix using matrix multiplication, equality of matrices, and a system of equations.

A)

B)

C)

D)

Question 67

Model the problem using a system of linear equations. Then solve using the augmented matrix. Suppose $24,000 is invested in three different accounts paying 3%, 4%, and 7%
Annual interest. The interest earned after 1 year is $1270, and the amount
Invested at 7% is equal to the sum of the amounts invested at 3% and 4%.
Find the amount invested at 3%.

A) $5000
B) $6000
C) $7000
D) $8000

Question 68

Perform the indicated operation, if possible. Do not use a calculator. If the operation cannot be completed, state why. 2A - 3B

Question 69

Find the values of a, b, and c that will make the statement true. =

Question 70

Perform the indicated operation, if possible. Do not use a calculator. If an operation cannot be completed, state why. A + B

A)

B)

C)

D) different orders, sum not possible

Question 71

Solve the system by triangularizing the augmented matrix and using back substitution. If the system is linearly dependent, give the solution in terms of a parameter.

A) (1, -3, 2)
B) (1, -3, 1)
C) coincident dependence; {(x, y, z) | 2x + y - 3z = -7}
D) no solution, inconsistent

Question 72

Perform the indicated operation(s), if possible. Do not use a calculator. If the operation cannot be completed, state why. AB and BA

Question 73

Perform the indicated operation, if possible. Do not use a calculator. If the operation cannot be completed, state why. A + B

Question 74

Solve the system by triangularizing the augmented matrix and using back substitution.

A) (-2, -2, -3)
B) (-2, -2, -2)
C) (-1, -3, -2)
D) (-1, -3, -3)

Question 75

Perform the indicated row operations, then write the new matrix.

A)

B)

C)

D)

Question 76

Solve the system by triangularizing the augmented matrix and using back substitution. If the system is linearly dependent, give the solution in terms of a parameter.

A) (0, 0, -3)
B) (0, 0, -2)
C) coincident dependence; {(x, y, z) | x - y + z = -2}
D) no solution, inconsistent

Question 77

What row operation would produce zero beneath the first entry in the diagonal?

Question 78

Solve the system by triangularizing the augmented matrix and using back substitution.

Question 79

Perform the indicated operation, if possible. Do not use a calculator. If the operation cannot be completed, state why. A + B

Question 80

Solve the system by triangularizing the augmented matrix and using back substitution.

A) (5, 5)
B) (6, 6)
C) (6, 5)
D) (5, 6)