Deck 3: Systems of Linear Equations

Question 1

Solve the equation graphically. 5 x + 8 = 3

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

Answer 1

x = -1

Question 2

Solve the system.

A)
B)
C)
D)
E)

Answer 2

Question 3

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

A) (5, 15)
B) ( x , y )
C) (2 x - y , 3 y - 6 x )
D) ( x , 2 x - 5)

Answer 3

( x , 2 x - 5)

Question 4

Solve the system.

A)
B)
C)
D)
E)

Question 5

Solve the equation graphically.

A)
B) x = 2
C)
D)

Question 6

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

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

Question 7

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

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

Question 8

Use the addition method to solve the system.

A)
B)
C)
D)
E)

Question 9

Solve the system by graphing.

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 10

Solve the equation graphically. 0.5 - 0.15 x = 0.2

A) (2, 0.2)
B) x = -1.4
C) x = -2
D) x = 2

Question 11

The following system is inconsistent.

Question 12

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.

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

Question 13

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

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

Question 14

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

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

Question 15

Solve the system by substitution method, if possible.

A)
B)
C)
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 16

Solve the system by graphing.

A)
B)
C)
D)

Question 17

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

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

Question 18

Solve the system by graphing.

A)
B)
C)
D)

Question 19

Solve the system.

A)
B)
C)
D)
E)

Question 20

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

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

Question 21

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

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

Question 22

Solve the system.

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

Question 23

The owner of a candy store mixed some peanuts worth $2 per pound, some cashews worth $8 per pound, and some Brazil nuts worth $8 per pound to get 50 pounds of a mixture that would sell for $5 per pound. She used 15 fewer pounds of cashews than peanuts. How many pounds of each did she use?

A) 15 lb peanuts, 10 lb cashews, 25 lb Brazil nuts
B) 15 lb peanuts, 20 lb cashews, 30 lb Brazil nuts
C) 25 lb peanuts, 10 lb cashews, 15 lb Brazil nuts
D) 30 lb peanuts, 15 lb cashews, 20 lb Brazil nuts
E) 10 lb peanuts, 25 lb cashews, 15 lb Brazil nuts

Question 24

Use two equations in two variables to solve the following problem. A rancher raises five times as many cows as horses. If he has 132 animals (cows and horses only), how many cows does he have?

A) 110 cows
B) 90 cows
C) 150 cows
D) 100 cows
E) 80 cows

Question 25

Solve the system.

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

Question 26

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

A)
B)
C)
D)

Question 27

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

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

Question 28

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.

A)
B)
C)
D) inconsistent

Question 29

Solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate.

Question 30

Write the repeating decimal as fraction. Simplify the answer when possible.

A)
B)
C)
D)

Question 31

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

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

Question 32

Solve the system.

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

Question 33

The sum of three integers is 18. The third integer is four times the second, and the second integer is 6 more than the first. Find the integers.

A) -2, 4, 16
B) 2, 4, 16
C) 2, 6, -12
D) -2, 6, 16
E) -4, 2, 16

Question 34

Select the fraction that accurately represents the repeating decimal. Simplify the answer if possible.

A)
B)
C)
D)
E)

Question 35

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?

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 36

Use two equations in two variables to solve the following problem. In a year the number of people dying from cancer was 5 times the number who died from accidents. If the number of deaths from these two causes totaled 360,000, how many people died from each cause?

A) 280,000 died from cancer, 60,000 died from accidents
B) 290,000 died from cancer, 70,000 died from accidents
C) 280,000 died from cancer, 80,000 died from accidents
D) 300,000 died from cancer, 60,000 died from accidents
E) 290,000 died from cancer, 80,000 died from accidents

Question 37

Write the repeating decimal as a fraction. Simplify the answer when possible.

A)
B)
C)
D)
E)

Question 38

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.

A)
B)
C) inconsistent
D)

Question 39

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.

A)
B)
C)
D) inconsistent

Question 40

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

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

Question 41

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

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

Question 42

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

A) ( 7, 5 )
B) ( 5, 3 )
C) ( 7, 3 )
D) ( 5, 5 )
E) No solution.

Question 43

Use matrices to help find a general solution of the system of equations. Express your answer in terms of z.

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

Question 44

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

Question 45

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.

Question 46

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

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

Question 47

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.

Question 48

Use Cramer's rule to find the solution set of the system.

A) x = -4, y = 6, z = -3
B) x = -6, y = 3, z = -3
C) x = -5, y = 4, z = -4
D) x = -4, y = 4, z = -4
E) x = -5, y = 5, z = -6

Question 49

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

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

Question 50

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

A) x = 7, y = 0
B) x = 4, y = 0
C) x = 2, y = 2
D) x = 3, y =2
E) x = 1, y = 5

Question 51

Evaluate the determinant.

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

Question 52

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

A) ( 3, 4, 6 )
B) ( 3, 4, 9 )
C) ( 3, 6, 6 )
D) ( 4, 6, 6 )
E) No solution.

Question 53

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

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

Question 54

Evaluate the determinant.

A) 27
B) -3
C) -27
D) -4
E) 3

Question 55

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.

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

Question 56

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?

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%