Deck 9: Systems of Linear Equations

Question 1

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
2x - 3y = 9 6x - 9y = 36

A) infinite number of solutions
B) no solution
C) one solution

Answer 1

no solution

Question 2

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
x + y = -4 x + y = 8

A) infinite number of solutions
B) no solution
C) one solution

Answer 2

no solution

Question 3

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
9x = 6y + 3 9x = 6y - 5

A) infinite number of solutions
B) no solution
C) one solution

Answer 3

no solution

Question 4

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
4x + 6y = 44 4x + 2y = 52

A) infinite number of solutions
B) no solution
C) one solution

Question 5

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
x + y = -50
Y = 9x

A) one solution
B) no solution
C) infinite number of solutions

Question 6

Determine if the following ordered pair satisfies the system of linear equations.

A) Yes
B) No

Question 7

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
6x - 4y = 2 -12x + 8y = -8

A) infinite number of solutions
B) no solution
C) one solution

Question 8

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.

A) inconsistent-no solution
B) dependent-infinite number of solutions
C) consistent-one solution

Question 9

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
5x - 7y = -9 5x - 7y = 9

A) infinite number of solutions
B) one solution
C) no solution

Question 10

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.

A) consistent-one solution
B) inconsistent-no solution
C) dependent-infinite number of solutions

Question 11

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.

A) inconsistent-no solution
B) dependent-infinite number of solutions
C) consistent-one solution

Question 12

Determine if the following ordered pair satisfies the system of linear equations.
(-6, -2) 4x + y = -22
3x + 4y = -10

A) Yes
B) No

Question 13

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.

A) consistent-one solution
B) dependent-infinite number of solutions
C) inconsistent-no solution

Question 14

Determine if the following ordered pair satisfies the system of linear equations.
(6, 2) 2x = -10 - y
3x = -14 - 2y

A) Yes
B) No

Question 15

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
x + y = -1 x - y = 11

A) no solution
B) one solution
C) infinite number of solutions

Question 16

Determine if the following ordered pair satisfies the system of linear equations.
(-2, 6) y = 4x + 14
Y = -3x

A) Yes
B) No

Question 17

Determine if the following ordered pair satisfies the system of linear equations.

A) Yes
B) No

Question 18

Determine if the following ordered pair satisfies the system of linear equations.
(-4, -3) x + y = 1
X - y = 7

A) Yes
B) No

Question 19

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.

A) dependent-infinite number of solutions
B) consistent-one solution
C) inconsistent-no solution

Question 20

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
y = x - 6 x - 5y = 30

A) no solution
B) one solution
C) infinite number of solutions

Question 21

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.

A) one solution
B) no solution
C) infinite number of solutions

Question 22

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
y - 4x = 5 5y = 20x + 25

A) one solution
B) no solution
C) infinite number of solutions

Question 23

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.

A) (-1.5, -1)
B) (1, 1)
C) dependent
D) inconsistent

Question 24

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
5x + y = 0 4x - 2y = -14

A) no solution
B) infinite number of solutions
C) one solution

Question 25

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
4x - 2y = -18 x = -4y

A) infinite number of solutions
B) one solution
C) no solution

Question 26

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.

A) (2, 0)
B) 12 , 0
C) dependent
D) inconsistent

Question 27

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.

A) (1, 1)
B) (1, 5)
C) dependent
D) inconsistent

Question 28

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.

A) (1, -8)
B) (-1, 8)
C) (-1, -8)
D) (1, 16)

Question 29

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.

A) no solution
B) one solution
C) infinite number of solutions

Question 30

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.

A) (0, 12)
B) (5, -3)
C) dependent
D) inconsistent

Question 31

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.

A) (3, 2)
B) (2, 3)
C) dependent
D) inconsistent

Question 32

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
y = 3x - 1 5y + 20x = 65

A) no solution
B) one solution
C) infinite number of solutions

Question 33

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.

A) (0,0)
B) (4, 5)
C) dependent
D) inconsistent

Question 34

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
-7y = x + 34 2x + 6y = -36

A) infinite number of solutions
B) no solution
C) one solution

Question 35

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.

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

Question 36

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.

A) no solution
B) one solution
C) infinite number of solutions

Question 37

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
2y = x + 24 2x + 4y = 0

A) no solution
B) one solution
C) infinite number of solutions

Question 38

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
2x + y = 8 8x + 4y = 32

A) one solution
B) no solution
C) infinite number of solutions

Question 39

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
-3x - 9y = -10 5x + 15y = 0

A) one solution
B) infinite number of solutions
C) no solution

Question 40

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
y y == 47x x -- 2 3

A) infinite number of solutions
B) one solution
C) no solution

Question 41

Find the solution by graphing the system of equations.
The Family Fine Arts Center charges $23 per adult and $12 per senior citizen for its performances. On a recent weekend evening when 446 people paid admission, the total receipts were $6485. We can represent this situation
With the system of equations
A + s = 446
23a + 12s = 6485
With a representing the adults who attended and s representing the senior citizens who attended. How many who paid
Were senior citizens?

A) 103 senior citizens
B) 253 senior citizens
C) 193 senior citizens
D) 343 senior citizens

Question 42

Find the solution to the system of equations by substitution.
x - y = -4

A) (0, 6)
B) (-1, 6)
C) (1, 5)
D) no solution

Question 43

Find the solution to the system of equations by substitution.

A) (4, 0)
B) (0, 4)
C) (-4, 0)
D) (0, -4)

Question 44

Find the solution to the system of equations by substitution.
y - 5x = 3 2y = 10x + 6

A) (-1.5, -1)
B) (1, 1)
C) infinite number of solutions
D) no solution

Question 45

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.

A) (6, 1)
B) (6, 0)
C) 6, 56
D) (0, 6)

Question 46

Find the solution to the system of equations by substitution.
x + y = -2 x - y = 12

A) 5, - 7
B) 2, - 7
C) 2, 5
D) 5, 7

Question 47

Find the solution to the system of equations by substitution.
x = -y y + x = 6

A) (1, 1)
B) (1, 5)
C) infinite number of solutions
D) no solution

Question 48

Find the solution by graphing the system of equations.
A shopkeeper ordered a total of 30 pounds of cashews and peanuts. He ordered 20 fewer pounds of cashews than peanuts. We can represent this situation with the system of equations
C + p = 30
P - c = 20
Where p represents the pounds of peanuts and c represents the pounds of cashews. How many pounds of peanuts did
He order?

A) 25 lb
B) 15 lb
C) 5 lb
D) 10 lb

Question 49

Find the solution to the system of equations by substitution.
9x + y = 0 -9x + y = -18

A) (1, 18)
B) (1, -9)
C) (-1, 9)
D) (-1, -9)

Question 50

Find the solution to the system of equations by substitution.

A) (100, -27)
B) (-100, -27)
C) (100, 27)
D) (-100, 27)

Question 51

Find the solution by graphing the system of equations.
A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 6 slices of pizza and 5 soft drinks for $28.45. The second group bought 5 slices of pizza and 5 soft drinks for $
25)10. We can represent this situation with the system of equations
6p + 5s = 28.45
5p + 5s = 25.10
Where p is the cost of a slice of pizza and s is the cost of a soft drink. Determine the cost of one slice of pizza.

A) $1.67 per slice of pizza
B) $3.35 per slice of pizza
C) $2.17 per slice of pizza
D) $2.85 per slice of pizza

Question 52

Find the solution to the system of equations by substitution.
x + 9y = 9 8x - 5y = -5

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

Question 53

Find the solution to the system of equations by substitution.
x - 5y = -28 x - 4y = -30

A) (1, 9)
B) (-2, 9)
C) (2, 8)
D) no solution

Question 54

Find the solution to the system of equations by substitution.
-4x + y = 14 -5x + 8y = 4

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

Question 55

Find the solution to the system of equations by substitution.
x + y = 0 2x + 3y = -7

A) (-7, 7)
B) (6, -6)
C) (-6, 6)
D) (7, -7)

Question 56

Find the solution by graphing the system of equations.
Sybil is having her yard landscaped. She obtained an estimate from two landscaping companies. Company A gave an estimate of $180 for materials and equipment rental plus $60 per hour for labor. Company B gave and
Estimate of $220 for materials and equipment rental plus $50 per hour for labor. We can represent this situation with
The system of linear equations
C = 180 + 60h
C = 220 + 50h
Where c is the total cost and h is the number of hours of labor. Find the number of hours of labor for the two companies
To have the same total cost.

A) 3 hr
B) 7 hr
C) 4 hr
D) 8 hr

Question 57

Find the solution to the system of equations by substitution.
x + 7y = -2 3x + y = 34

A) (3, 7)
B) (7, 12)
C) (12, -2)
D) (-2, 3)

Question 58

Find the solution to the system of equations by substitution.
y = 3x + 3 y = 8x + 2

A)
B)
C) infinite number of solutions
D) no solution

Question 59

Find the solution to the system of equations by substitution.
x - 5y = -4 x + 8y = -4

A) (4, 0)
B) (-4, 0)
C) (0, 4)
D) (0, -4)

Question 60

Find the solution to the system of equations by substitution.
x y -= 2-y 3 = 11

A) (-3, 5)
B) (5, -3)
C) (17, -3)
D) (-5, -3)

Question 61

Solve the system of equations using the addition method.
2x - 2y = 9 10x - 10y = 18

A)
B) (9, 18)
C) infinite number of solutions
D) no solution

Question 62

Solve the system of equations using the addition method.
2x + 40y = 40 4x - 5y = -5

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

Question 63

Solve the problem.
On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $8 each and a number of necklaces at $10 each. She wrote a check for $1160 to pay for the order. How many bracelets
And how many necklaces did Rosaria purchase?

A) 30 bracelets and 90 necklaces
B) 25 bracelets and 95 necklaces
C) 20 bracelets and 100 necklaces
D) 15 bracelets and 105 necklaces

Question 64

Solve the problem.
Devon purchased tickets to an air show for 4 adults and 2 children. The total cost was $144. The cost of a child's ticket was $3 less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket.

A) adult's ticket: $24; child's ticket: $21
B) adult's ticket: $27; child's ticket: $24
C) adult's ticket: $26; child's ticket: $23
D) adult's ticket: $25; child's ticket: $22

Question 65

Solve the problem.
One number is four more than a second number. Two times the first number is 4 more than four times the second number.

A) - 6 and - 10
B) 6 and 2
C) 5 and 1
D) 7 and 3

Question 66

Find the solution to the system of equations by substitution.

A) (5, 2)
B) (-5, -2)
C) (-5, 2)
D) (5, -2)

Question 67

Solve the system of equations using the addition method.
x - 5y = 3 x - 5y = 3

A)
B)
C) infinite number of solutions
D) no solution

Question 68

Solve the system of equations using the addition method.
6x + 5y = -4 -6x - 11y = 16

A) (6, 2)
B) (-6, -2)
C) (-1, 2)
D) (1, -2)

Question 69

Solve the system of equations using the addition method.
8x - 5y = 5 -16x + 10y = -20

A) (2, 4)
B)
C) (8, 5)
D) no solution

Question 70

Solve the problem.
A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 3 bags of potato chips for $12.50. Another customer buys 2 hot dogs and 3 bags of potato chips for $8.50. Find the cost of each item.

A) $2.00 for a hot dog; $1.75 for a bag of potato chips
B) $1.50 for a hot dog; $2.00 for a bag of potato chips
C) $2.25 for a hot dog; $1.75 for a bag of potato chips
D) $2.00 for a hot dog; $1.50 for a bag of potato chips

Question 71

Solve the system of equations using the addition method.
6x + 4y = 48 6x + 2y = 60

A) (12, -6)
B) (-6, 12)
C) (-12, 4)
D) (-12, 6)

Question 72

Solve the system of equations using the addition method.
x + 8y = -53 -6x + 7y = -12

A) (5, -5)
B) (-5, -6)
C) (-6, -5)
D) no solution

Question 73

Solve the problem.
One number is 5 less than a second number. Twice the second number is 4 less than 4 times the first. Find the two numbers.

A) 7 and 12
B) 6 and 11
C) -12 and -7
D) 8 and 13

Question 74

Solve the problem.
Two numbers total 8, and their difference is 16. Find the two numbers.

A) 4 and - 12
B) 8 and 2
C) 12 and - 4
D) 5 and 3

Question 75

Solve the system of equations using the addition method.
2x + 24y = -110 8x + 6y = 10

A) (-6, 5)
B) (8, -8)
C) (-5, 5)
D) (5, -5)

Question 76

Solve the problem.
Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 9 times as many dimes as nickels, and the value of the dimes is $9.35 more
Than the value of the nickels. How many nickels and dimes does Jamil have?

A) 11 nickels and 99 dimes
B) 10 nickels and 90 dimes
C) 12 nickels and 108 dimes
D) 99 nickels and 11 dimes

Question 77

Solve the system of equations using the addition method.

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

Question 78

Solve the problem.
Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 7 feet more than 3 times the width. He needs 46 feet of fencing to do the job. Find the length and
Width of the garden.

A) length: 22 ft; width: 5 ft
B) length: 16 ft; width: 3 ft
C)
D) length: 19 ft; width: 4 ft

Question 79

Solve the problem.
One number is 5 less than a second number. Twice the second number is 52 more than 5 times the first. Find the two numbers.

A) -13 and -8
B) -14 and -9
C) 9 and 14
D) -15 and -10

Question 80

Solve the problem.
A bank teller has both $10 and $20 bills in her cash drawer. There are 31 $20 bills, and the total amount of all the bills is $740. How many $10 bills are there?

A) 12 $10 bills
B) 14 $10 bills
C) 31 $10 bills
D) 29 $10 bills