Deck 4: Systems of Linear Equations

Question 1

Graph the system of linear inequalities. Label the solution region.

-

A)

B)
C)
D)
E) none of these

Answer 1

Question 2

Graph the system of linear inequalities. Label the solution region.

-

A)
B)
C)
D)
E) none of these

Answer 2

Question 3

Graph the system of linear inequalities. Label the solution region.

-

A)
B)
C)
D)
E) none of these

Answer 3

Question 4

Graph the system of linear inequalities. Label the solution region.

-

A)
B)
C)
D)
E) none of these

Question 5

The graph represents a system of linear inequalities. Estimate the vertices.

A)
B)
C)
D)
E) none of these

Question 6

The graph represents a system of inequalities. Estimate the vertices.

A)
B)
C)
D)
E) none of these

Question 7

Use an algebraic method to find the vertices of the system of linear inequalities.

A)
B)
C)
D)
E) none of these

Question 8

Use an algebraic method to determine which, if any, of the ordered pairs is a solution to the system of inequalities.

A)
B)
C)
D)
E) none of these

Question 9

Use the system of inequalities.

-Graph the system.

A)
B)
C)
D)
E) none of these

Question 10

Use the system of inequalities.

-Use an algebraic method to find the vertices.

A)
B)
C)
D)
E) none of these

Question 11

Use the system of inequalities.

-Graph the system of inequalities.

A)
B)
C)
D)
E) none of these

Question 12

Use the system of inequalities.

-Use an algebraic method to find the vertices.

A)
B)
C)
D)
E) none of these

Question 13

An investor can invest at most $20,000 in a retirement plan. He wants to place at least $5000 in Treasury Notes yielding 5% and more than $14,000 in corporate bonds yielding 8%. He also wants to earn $1420 annually. Let
the amount invested in Treasury Notes and the amount invested in corporate bonds.

-Write four constraints that describe this situation.

A)
B)
C)
D)
E) none of these

Question 14

An investor can invest at most $20,000 in a retirement plan. He wants to place at least $5000 in Treasury Notes yielding 5% and more than $14,000 in corporate bonds yielding 8%. He also wants to earn $1420 annually. Let
the amount invested in Treasury Notes and the amount invested in corporate bonds.

-Graph the constraints.

A)
B)
C)
D)
E) none of these

Question 15

An investor can invest at most $20,000 in a retirement plan. He wants to place at least $5000 in Treasury Notes yielding 5% and more than $14,000 in corporate bonds yielding 8%. He also wants to earn $1420 annually. Let
the amount invested in Treasury Notes and the amount invested in corporate bonds.

-Estimate the vertices of the feasible region.

A)
B)
C)
D)
E) none of these

Question 16

Represent the system of equations with an augmented matrix:

A)
B)
C)
D)
E) none of these

Question 17

Represent the system of equations with an augmented matrix:

A)
B)
C)
D)
E) none of these

Question 18

Use row operations to change the first entry in the first row to 1. Rewrite the matrix.

A)
B)
C)
D)
E) none of these

Question 19

The matrix represents a system of equations in reduced row echelon form. Identify the solution of the system of equations.

A)(1, 0)
B)(-9, 4)
C) (4, -9)
D) infinitely many solutions
E) no solution

Question 20

The matrix represents a system of equations in reduced row echelon form. Identify the solution of the system of equations.

A) (2, 0, -1)
B) (1, 0, 0)
C) (-1, 0, 2)
D) infinitely many solutions
E) no solution

Question 21

The matrix represent a system of equations in reduced row echelon form. Identify the solution of the system of equations.

A) (0, 0, 0)
B) (5, 3, 6)
C) (5, 3, 0)
D) infinitely many solutions
E) no solution

Question 22

Use row operations to change the first entry in the second row to 0. Rewrite the matrix.

A)
B)
C)
D)
E) none of these

Question 23

Use row operations to change the first entry in the second row to 0. Rewrite the matrix

A)
B)
C)
D)
E) none of these

Question 24

Represent the system of equations with an augmented matrix. Solve the system by rewriting the matrix in reduced row echelon form.

-

A)(5, 8)
B) (-5, 8)
C) ( 5, -60
D) infinitely many solutions
E) no solution

Question 25

Represent the system of equations with an augmented matrix. Solve the system by rewriting the matrix in reduced row echelon form.

-

A) (4, -1)
B) (-5, 1)
C) ( -4, 1)
D) infinitely many solutions
E) no solution

Question 26

Represent the system of equations with an augmented matrix. Solve the system by rewriting the matrix in reduced row echelon form.

-

A) (0, 20)
B) (0, 0)
C) (2, 0)
D) infinitely many solutions
E) no solution

Question 27

Represent the system of equations with an augmented matrix. Solve the system by rewriting the matrix in reduced row echelon form.

-

A) (3, -4, 1)
B) (-3, 4, 10
C)
D) infinitely many solutions
E) no solution

Question 28

Represent the system of equations with an augmented matrix. Solve the system by rewriting the matrix in reduced row echelon form.

-

A)
B) ( 11, -22, 6)
C)
D) infinitely many solutions
E) no solution

Question 29

Represent the system of equations with an augmented matrix. Solve the system by rewriting the matrix in reduced row echelon form.

-

A)(-3, -3, -3)
B) (-4, 0, 3)
C) ( -2, -8, 6)
D) infinitely many solutions
E) no solution

Question 30

Students are having a bake sale to raise funds for the school band. They collect $19.00 for selling 2 pies, 1 cake, and 3 cinnamon rolls. They collect $11.50 for selling 1 cake and 4 cinnamon rolls. They collect $17.50 for selling 1 pie, 1 cake and 5 cinnamon rolls. Find the price for each item.

A) $4.00 per pie$3.50 per cake$2.00 per cinnamon roll
B) $4.50 per pie$5.50 per cake$1.50 per cinnamon roll
C) $5.50 per pie$4.50 per cake$1.50 per cinnamon roll
D) $4.25 per pie$7.50 per cake$1.00 per cinnamon roll
E) none of these

Question 31

Use an algebraic method to determine which of the ordered triples is a solution to the system.

A)
B)
C)
D)
E) none of these

Question 32

Use an algebraic method to determine which of the ordered triples is a solution to the system.

A)
B)
C)
D)
E) none of these

Question 33

Use constant multiples of only the top equation to eliminate the variable x from the system of equations. Which system of two equations results?

A)
B)
C)
D)
E) none of these

Question 34

Use constant multiples of only the top equation to eliminate the variable y from the system of equations. Which system of two equations results?

A)
B)
C)
D)
E) none of these

Question 35

Use constant multiples of only the top equation to eliminate the variable z from the system of equations. Which system of two equations results?

A)
B)
C)
D)
E) none of these

Question 36

Solve the system of equations using elimination, if possible, and express the solution as an ordered triple.

-

A)
B)
C)
D) infinitely many solutions
E) no solution

Question 37

Solve the system of equations using elimination, if possible, and express the solution as an ordered triple.

-

A)
B)
C)
D) infinitely many solutions
E) no solution

Question 38

Solve the system of equations using elimination, if possible, and express the solution as an ordered triple.

-

A)
B)
C)
D) infinitely many solutions
E) no solution

Question 39

Solve the system of equations using elimination, if possible, and express the solution as an ordered triple.

-

A)
B)
C)
D) infinitely many solutions
E) no solution

Question 40

Solve the system of equations using elimination, if possible, and express the solution as an ordered triple.

-

A)
B)
C)
D) infinitely many solutions
E) no solution

Question 41

Solve the system of equations using elimination, if possible, and express the solution as an ordered triple.

-

A)
B)
C)
D) infinitely many solutions
E) no solution

Question 42

Solve the system of equations using elimination, if possible, and express the solution as an ordered triple.

-

A)
B)
C)
D) infinitely many solutions
E) no solution

Question 43

Nancy just inherited $83,000. She decides to diversify her investment by putting the money into three different accounts: tax-free bonds which pay 5% annual interest, a certificate of deposit which pays 7% annual interest, and a mutual stock fund which has an average annual rate of return of 12%. The amount she invests in the certificate of deposit is double the amount she invests in bonds. Her goal for total return per year from these three investments is $7720. How much should Nancy put into each account?

A)
B)
C)
D)
E) none of these

Question 44

In the Storms baseball stadium, there are three levels of seats available. Box seats are sold for $10 each, reserved seats are sold for $7 each, and bleacher seats are sold for $4 each. The stadium capacity is 4500. Total revenue is $27,900 when all seats are sold. If half the box seats, half the reserved seats, and all of the bleacher seats are sold, the revenue is $18,150. Find how many of each type of seat are there.

A)
B)
C)
D)
E) none of these

Question 45

Morgan is keeping track of her calcium intake from three sources for three days. The first day she had a glass of milk, a serving of cottage cheesem and 1 calcium supplement pill totaling 1090 mg of calcium. The second day she had 2 glasses of milk, 1 serving of cottage cheese, and 1 calcium supplement totaling 1450 mg of calcium. The third day she had 1 glass of milk, 2 servings of cottage cheese, and 1 calcium supplement totaling 1310 mg of calcium. Find the amount of calcium in each of the three sources.

A)
B)
C)
D)
E) none of these

Question 46

A company that manufactures gas grills sells their lowest-end grill for . It costs to manufacture each grill and the company has an overhead cost of per month.

-Find the number of grills that must be sold each month to break even.

A)
B)
C)
D)
E) none of these

Question 47

A company that manufactures gas grills sells their lowest-end grill for . It costs to manufacture each grill and the company has an overhead cost of per month.

-Find the grill-manufacturer's revenue at the break-even point.

A)
B)
C)
D)
E) none of these

Question 48

Chloe decides to open a lemonade stand to earn money for the summer. She is able to build a lemonade stand for $49. To make each cup of lemonade, including the cost of the cup, costs $0.12. She decides to sell each cup for $0.40. How many cups of lemonade must Chloe sell to break even?

A) 123
B) 62
C) 175
D) 70
E) none of these

Question 49

Find Chloe's revenue at the break-even point.

A) $175
B) $70
C) $24.80
D) $49.20
E) none of these

Question 50

Suppose that you receive an inheritance of $48,000. You decide to invest some of the money in stocks and some in certificates of deposit (CDs). Because the CDs are a less risky investment you want to put 3 times as much into CDs as stocks. How much are you going to invest in each type of account?

A)
B)
C)
D)
E) none of these

Question 51

The cost of 5 deli sandwiches and 7 small salads is . The cost of 6 deli sandwiches and 4 small salads is
. Find the cost of the deli sandwich and the small salad.

A)
B)
C)
D)
E) none of these

Question 52

A metallurgist has an alloy with 12% titanium and an alloy with 44% titanium. He needs 100 grams of an alloy with 20% titanium. How much of each alloy should be mixed to obtain the 100 grams of alloy with 20% titanium?

A)
B)
C)
D)
E) none of these

Question 53

The owner of a coffee shop is making a special blend of coffee that combines Ethiopian beans that sell for Per pound and Guatemalan beans that sell for Per pound. She wants to have a total of Pounds of the special blend, and she is selling it for Per pound. How many pounds of each type of bean should she combine?

A)
B)
C)
D)
E) none of these

Question 54

Two blends will be used to make ice cream that contains 10% milkfat. Blend A contains 6% milkfat and blend B contains 13% milkfat. How much of each blend should be used to make 2000 gallons of ice cream that contains 10% milkfat?

A)
B)
C)
D)
E) none of these

Question 55

One cell phone plan charges $35.99 per month, including 400 minutes of out-of-network calls each month. Each additional minute outside the network costs $0.25. Another plan charges $59.99 per month, including 1000 minutes of out-of-network calls per month. This plan charges $0.40 for each additional minute out of the network. Find the number of total minutes outside the network a customer must use for the plans to cost the same in a month.

A) 1840
B) 1400
C) 1000
D) 400
E) none of these

Question 56

Sally and Harry go to a fast food restaurant for breakfast. Sally ordered Sausage biscuit sandwiches and Orange juice. Her meal contained Grams of carbohydrates. Harry ordered Sausage biscuit sandwiches and Orange juices and his meal contained Grams of carbohydrates. How many carbohydrates are in the each sausage biscuit and in each orange juice?

A)
B)
C)
D)
E) none of these

Question 57

Sean is shifting his debt on his credit cards. He wants 4 times as much on his Visa card as on his Mastercard. Find the amount of debt he should have on each card.

A)
B)
C)
D)
E) none of these

Question 58

A Saturday matinee sells adult tickets for $6.50 and kid tickets, for kids under 12, for $4.00. A total of 150 tickets were sold, and the revenue from the ticket sales was $805. Find the number of adult tickets and the number of kid tickets sold.

A)
B)
C)
D)
E) none of these

Question 59

Two bicyclists leave the same point at the same time and travel in opposite directions. One cyclist rides at an average speed of 9 mph and the other at an average speed of 12 mph. Find the distance each cyclist has gone when the distance between them is 22 miles. Round your answer to the nearest tenth of a mile.

A)
B)
C)
D)
E) none of these

Question 60

Miley is shifting her credit card debt. She has a total of $2292 in debt, and she wants three times as much debt on her Visa as on her Master Card. How much debt will she have on each credit card?

A)
B)
C)
D)
E) none of these

Question 61

Solve the equation For the variable

A)
B)
C)
D)
E) none of these

Question 62

Write the system of equations in standard from, clearing all fractions:

A)
B)
C)
D)
E) none of these

Question 63

Solve the system of equations by substitution.

-

A) {-3 ,5}
B) {3 , -5}
C) {0 , 4}
D) infinitely many solutions
E) no solution

Question 64

Solve the system of equations by substitution.

-

A) {-1 , }
B) {-6 ,-7}
C) { 6 ,-7}
D) infinitely many solutions
E) no solution

Question 65

Solve the system of equations by substitution.

-

A) {-1 ,5}
B) {0 ,-5}
C) {5 ,0 }
D) infinitely many solutions
E) no solution

Question 66

Solve the system of equations by substitution.

-

A) {7 ,-11}
B) {7 ,-9}
C) {8 ,-11}
D) infinitely many solutions
E) no solution

Question 67

Solve the system of equations by substitution.

-

A) {35 ,35 }
B) {0 , }
C) { , 0}
D) infinitely many solutions
E) no solution

Question 68

Use elimination to solve the system of equations.

-

A) {1 ,3}
B) {-1 ,3}
C) {8 ,3}
D) infinitely many solutions
E) no solution

Question 69

Use elimination to solve the system of equations.

-

A) {0 ,3}
B) {-12 ,3}
C) {0 ,-3}
D) infinitely many solutions
E) no solution

Question 70

Use elimination to solve the system of equations.

-

A) { }
B) { }
C) { }
D) infinitely many solutions
E) no solution

Question 71

Use elimination to solve the system of equations.

-

A) { }
B) { }
C) { }
D) infinitely many solutions
E) no solution

Question 72

Use elimination to solve the system of equations.

-

A) {272 , 84}
B) {544 , -840}
C) {84 , 272}
D) infinitely many solutions
E) no solution

Question 73

Solve the system using any method.

-

A) {0 , 0}
B) { }
C){ }
D) infinitely many solutions
E) no solution

Question 74

Solve the system using any method.

-

A) {2 , -4}
B) {-2 , 10}
C) { }
D) infinitely many solutions
E) no solution

Question 75

Solve the system using any method.

-

A) { }
B) { }
C) { }
D) infinitely many solutions
E) no solution

Question 76

Use an algebraic method to determine for which, if any, system {-2 , -4} is a solution.

A)
B)
C)
D)
E) none of these

Question 77

Use an algebraic method to determine for which, if any, system {6 , -2} is a solution.

A)
B)
C)
D)
E) none of these

Question 78

Use an algebraic method to determine for which, if any, system {-3 , 2} is a solution.

A)
B)
C)
D)
E) none of these

Question 79

The graph represents the system of equations
. Solve by graphing.

A) {-3 , 0}
B) {0 , -3}
C) {1 , -1}
D) {-3 , 0}.
E) no solution

Question 80

The graph represents the system of equations
. Solve by graphing.

A) {-1 , -2}
B) {2 , -1}
C) {-2, -1}
D) {-1 , 2}
E) no solution