Deck 8: Systems of Equations and Inequalities

Question 1

Solve the system by inspecting the graph of the equations.
16x - 4y = -8 y = 4x + 2

A)
B)
C) (x, y) y = 4x + 2
D) (0, 2)

Answer 1

(x, y) y = 4x + 2

Question 2

Solve the system by graphing.
3x - 2y = 4 -6x + 4y = 7

A) {(2, 1)}
B)
C) {(1, 2)}
D) {(x, y) | -6x + 4y = 7}

Answer 2

Question 3

Solve the system by graphing.
3x + y = 10 12x + 4y = 40

A) {(5, -5)}
B) {(x, y) | 3x + y = 10}
C)
D) {(0, 10)}

Answer 3

{(x, y) | 3x + y = 10}

Question 4

Solve the system by substitution.
x + y = 4 x - y = -8

A) {(-3, 7)}
B)
C) {(-2, 6)}
D) {(2, 7)}

Question 5

Solve the system by graphing.
3x + 2y = 5 -6x - 4y = 5

A)
B) {(1, 1)}
C) {(1.5, -1)}
D) {(-1.5, -1)}

Question 6

Solve the system by substitution.
5x + 5y = 6 4x + 4y = 8

A) {(x, y) | 5x + 5y = 6}
B)
C) {(1, 1)}
D) {(9, 4)}

Question 7

Determine whether the given point is in the solution set to the given system.
(-3, 6) 3x + y = -3
2x + 3y = 12

A) Yes
B) No

Question 8

Solve the system by substitution.
x + 4y = -9 2x + 4y = -6

A) {(4, -4)}
B) {(3, -3)}
C) {(4, 3)}
D)

Question 9

Solve the system by inspecting the graph of the equations.
x + 4y = -15 2x - 2y = 20

A) (4, -5)
B)
C) (5, -5)
D) (5, -4)

Question 10

Determine whether the given point is in the solution set to the given system.
(5, 3) 4x + y = 17
3x + 4y = 3

A) Yes
B) No

Question 11

Determine whether the given point is in the solution set to the given system.
(4, 3) x + y = 7
X - y = 1

A) Yes
B) No

Question 12

Solve the system by graphing.
3x + y = -11 3x + 5y = 5

A) {(-5, 4)}
B) {(-3, -2)}
C) {(5, 4)}
D) {(-5, -6)}

Question 13

Solve the system by graphing.

A) {(3, 4)}
B) {(3, 1)}
C) {(4, 3)}
D) {(4, -3)}

Question 14

Solve the system by graphing.
3x + y = 19 3x + y = 25

A) {(15, -26)}
B) {(12, 7)}
C)
D) {(x, y) | 3x + y = 19}

Question 15

Solve the system by substitution.
3x - 9y = -21 2x + 3y = 22

A) {(-5, 4)}
B)
C) {(5, 4)}
D) {(-8, -2)}

Question 16

Determine whether the given point is in the solution set to the given system.
(-4, 6) x + y = 10
X - y = -2

A) No
B) Yes

Question 17

Solve the system by graphing.
2x - 2y = 4 -2x + 2y = -4

A) {(2, 0)}
B)
C) {(8, 6)}
D) {(6, 8)}

Question 18

Solve the system by substitution.
8x + 7y = 2 8x + 7y = 15

A)
B) {(x, y) | 8x + 7y = 2}
C) {(1, 1)}
D) {(8, 7)}

Question 19

Solve the system by graphing.
x = -y y + x = 6

A) {(1, 5)}
B)
C) {(1, 1)}
D) {(x, y) | y + x = 6}

Question 20

Solve the system by substitution.
x + 5y = 0 x - 5y = 90

A) {(45, 9)}
B) {(5, -1)}
C) {(45, -9)}
D) {(-9, 45)}

Question 21

Solve the system by addition.
9x - 99 = 9y -3x - 5y = -9

A) {(8, -3)}
B)
C) {(8, -2)}
D) {(7, -2)}

Question 22

Solve the system by addition.
x + 2y = 5 3x + 1y = 20

A) {(7, -1)}
B)
C) {(-7, 0)}
D) {(6, 0)}

Question 23

Classify the system as independent, inconsistent, or dependent.
x - 3y = 6 3y + 1 = x

A) Independent
B) Dependent
C) Inconsistent

Question 24

Solve the system by substitution.
2y = 3x - 7

A) (x, y) 2y = 3x - 7
B)
C)
D)

Question 25

Classify the system as independent, inconsistent, or dependent.
x - 1 = y y + 2 = x

A) Independent
B) Dependent
C) Inconsistent

Question 26

Classify the system as independent, inconsistent, or dependent.
3x = y + 3 6x - 2y = 3

A) Dependent
B) Independent
C) Inconsistent

Question 27

Solve the system by addition.
0.2x + 0.05y = 0.15 4x + y = 3

A) (x, y) 4x + y = 3
B)
C) (0, 3)
D)

Question 28

Solve the system by addition.
x - 2y = -16 -7x - 1y = -8

A) {(-8, 0)}
B)
C) {(1, 7)}
D) {(0, 8)}

Question 29

Solve the system by addition.
-7x + 7y = -49 3x - 5y = 21

A) {(7, 0)}
B)
C) {(6, 1)}
D) {(7, 1)}

Question 30

Solve the system by substitution.
= 4 2y = 21

A) {(-6, -8)}
B) {(6, -8)}
C) {(6, 8)}
D) {(-6, 8)}

Question 31

Solve the system by addition.
3 = 7

A)
B) (18, 0)
C) (0, 24)
D)

Question 32

Solve the system by addition.
7x + 9y = -45 4x + 6y = -30

A) {(0, -5)}
B) {(0, -4)}
C) {(-1, -4)}
D)

Question 33

Solve the system by substitution.
0.02x + 0.01y = -0.01 -0.01x + y = 3.02

A) {(-0.2, 0.3)}
B) {(3, -2)}
C)
D) {(-2, 3)}

Question 34

Solve the system by substitution.
0.6x + 0.7y = -0.2 x - 0.7y = -7.8

A) {(-5, 4)}
B) {(4, -5)}
C) {(-0.5, 0.4)}
D)

Question 35

Solve the system by addition.
= -18 = -9

A) {(-12, 0)}
B) {(0, -12)}
C) {(0, 12)}
D) {(12, 0)}

Question 36

Classify the system as independent, inconsistent, or dependent.
2x - y = 5 -4x + 2y = -18

A) Dependent
B) Inconsistent
C) Independent

Question 37

Solve the system by addition.
7x + 8y = -62 14x = -64 - 16y

A) {(-2, -6)}
B) {(-2, 9)}
C)
D) {(7, 9)}

Question 38

Solve the system by addition.
-7x + 9y = 50 -4x + 7y = 36

A)
B) {(-2, 5)}
C) {(-3, 5)}
D) {(-2, 4)}

Question 39

Classify the system as independent, inconsistent, or dependent.
2x - y = 4 x + 3y = 2

A) Inconsistent
B) Independent
C) Dependent

Question 40

Classify the system as independent, inconsistent, or dependent.
x + y = 2 x + y = 5

A) Independent
B) Dependent
C) Inconsistent

Question 41

For the given pair of points, find the equation of the line y = ax + b that goes through the points by solving a system of
equations.
(-8, -7) and (-7, -6)

A) y = -x - 7
B) y = x - 15
C) y = -x + 1
D) y = x + 1

Question 42

For the given pair of points, find the equation of the line y = ax + b that goes through the points by solving a system of
equations.
(-3, -1) and (6, 26)

A) y = 3x + 8
B) y = 3x - 10
C) y = 6x + 8
D) y = 3x - 1

Question 43

Solve the problem.
The perimeter of a rectangle is 42 cm. One side is 9 cm longer than the other side. Find the lengths of the sides.

A) 8 cm, 17 cm
B) 6 cm, 15 cm
C) 12 cm, 21 cm
D) 6 cm, 9 cm

Question 44

For the given pair of points, find the equation of the line y = ax + b that goes through the points by solving a system of
equations.
(-3, 2) and (-5, 6)

A) y = -2x - 4
B) y = -2x + 8
C) y = -4x - 4
D) y = -2x + 2

Question 45

For the given pair of points, find the equation of the line y = ax + b that goes through the points by solving a system of
equations.
(3, 1) and (4, 3)

A) y = 2x - 5
B) y = 4x - 5
C) y = 2x + 1
D) y = 2x + 7

Question 46

For the given pair of points, find the equation of the line y = ax + b that goes through the points by solving a system of
equations.
(3, 2) and (4, 3)

A) y = x + 2
B) y = -x - 1
C) y = x + 5
D) y = x - 1

Question 47

Classify the system as independent, inconsistent, or dependent.
-5 = 7x + 7y -21y - 21x = 15

A) Inconsistent
B) Independent
C) Dependent

Question 48

Solve the problem.
Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $96 for 3 days and 300 miles, while Mary was charged $169 for 5 days and 600 miles. What does Best Rental charge per day and
Per mile?

A) $22 per day, 10¢ per mile
B) $23 per day, 9¢ per mile
C) $24 per day, 10¢ per mile
D) $9 per day, 23¢ per mile

Question 49

Solve the problem.
The perimeter of a rectangle is 66 m. If the width were doubled and the length were increased by 24 m, the perimeter would be 132 m. What are the length and width of the rectangle?

A) width 16 m, length 16 m
B) width 11 m, length 16 m
C) width 24 m, length 9 m
D) width 9 m, length 24 m

Question 50

Solve the problem.
There were 450 people at a play. The admission price was $3 for adults and $1 for children. The admission receipts were $870. How many adults and how many children attended?

A) 217 adults, 233 children
B) 240 adults, 210 children
C) 120 adults, 330 children
D) 210 adults, 240 children

Question 51

For the given pair of points, find the equation of the line y = ax + b that goes through the points by solving a system of
equations.
(9, -7) and (8, -4)

A) y = -3x + 20
B) y = 3x - 20
C) y = -3x - 7
D) y = 3x - 34

Question 52

Solve the system by graphing the equations on a graphing calculator and estimating the point of intersection. Round to
the nearest hundredth.
-7.86x - 3.48y = 8 5.38x - 7.63y = 3

A) {(0.64, 0.85)}
B) {(0.85, -0.64)}
C) {(-0.85, -0.64)}
D) {(-0.64, -0.85)}

Question 53

For the given pair of points, find the equation of the line y = ax + b that goes through the points by solving a system of
equations.
(2, -1) and (-5, 6)

A) y = -x - 3
B) y = x + 1
C) y = -x - 1
D) y = -x + 1

Question 54

For the given pair of points, find the equation of the line y = ax + b that goes through the points by solving a system of
equations.
(3, -2) and (-3, 16)

A) y = 3x - 11
B) y = 3x + 7
C) y = -3x + 7
D) y = -3x - 2

Question 55

Solve the problem.
There were 35,000 people at a ball game in Los Angeles. The day's receipts were $245,000. How many people paid $11 for reserved seats and how many paid $6 for general admission?

A) 26,250 people paid $11 and 8750 people paid $6
B) 28,000 people paid $11 and 7000 people paid $6
C) 7000 people paid $11 and 28,000 people paid $6
D) 8750 people paid $11 and 26,250 people paid $6

Question 56

Classify the system as independent, inconsistent, or dependent.
-1 = 6x + 7y 14y + 12x = -3

A) Dependent
B) Independent
C) Inconsistent

Question 57

Solve the problem.
The perimeter of a triangle is 33 cm. The triangle is isosceles now, but if its base were lengthened by 4 cm and each leg were shortened by 2 cm, it would be equilateral. Find the base of the original triangle.

A) 13 cm
B) 6 cm
C) 7 cm
D) 11 cm

Question 58

For the given pair of points, find the equation of the line y = ax + b that goes through the points by solving a system of
equations.
(-8, -8) and (-7, -6)

A) y = 2x + 8
B) y = 2x - 24
C) y = 4x + 8
D) y = 2x - 8

Question 59

Solve the problem.
A salesman sold $150 more than the rest of the sales staff. If the sales total for the day was $2300, how much did the rest of the sales staff sell?

A) $1075
B) $1150
C) $2150
D) $1225

Question 60

Solve the problem.
A shopkeeper orders 30 pounds of cashews and peanuts. If he orders 24 less pounds of cashews, how many pounds of peanuts did he order?

A) 6 lb
B) 3 lb
C) 27 lb
D) 15 lb

Question 61

Determine whether the given point is in the solution set to the given system.
(7, 2, -5) 3x - 8y + z = 0
2x + 4y - 3z = 37
-x + 2y - z = 2

A) Yes
B) No

Question 62

Determine whether the given point is in the solution set to the given system.
(-2, -1, 5) x - y + z = 4
2x - 8y - 3z = 24
3x + 4y + 2z = 7

A) No
B) Yes

Question 63

Select the graph that represents the given equation.
x + y + z = 6

A)
B)
C)
D)

Question 64

Determine whether the given point is in the solution set to the given system.
9x + 6y + 9z = 5 6x + 3y - 3z = 14
X - y + 2z = -3

A) Yes
B) No

Question 65

Determine whether the given point is in the solution set to the given system.
9x - 9y - 6z = -11 6x + 3y - 3z = 1
X - y + 2z = -3

A) No
B) Yes

Question 66

Determine whether the given point is in the solution set to the given system.
3x - 2y + 3z = 17 x + 4y - 2z = -8
2x - y + z = 8

A) Yes
B) No

Question 67

Solve the system of equations.
x - y + 4z = -5 2x + z = 0
X + 2y + z = 10

A)
B) {(0, 5, 0)}
C) {(0, 0, 5)}
D) {(0, 5, -5)}

Question 68

Select the graph that represents the given equation.
x + 2y - z = 4

A)
B)
C)
D)

Question 69

Determine whether the given point is in the solution set to the given system.
(-2, 6, -1) -x + 3y + 4z = 16
3x + 2y - z = 7
4x - y + 3z = -17

A) Yes
B) No

Question 70

Find the ordered triple that belongs to the set.
{x, x + 4, x - 7|x = 1}

A) (-6, 1, 5)
B) (1, -6, 5)
C) (1, 5, -6)
D) (-6, 5, 1)

Question 71

Solve the system of equations.
x + y + z = 4 x - y + 3z = 10
4x + y + z = -5

A) {(-3, 2, 5)}
B) {(5, -3, 2)}
C) {(5, 2, -3)}
D)

Question 72

For the given pair of points, find the equation of the line y = ax + b that goes through the points by solving a system of
equations.
(-2, -3) and (6, 5)

A) y = x - 3
B) y = -2x - 1
C) y = x - 5
D) y = x - 1

Question 73

Determine whether the given point is in the solution set to the given system.
(-3, -1, 4) 2x - 2y - 3z = -16
4x - 3y + 3z = 3
X + y - 5z = -24

A) No
B) Yes

Question 74

Determine whether the given point is in the solution set to the given system.
(2, 8, -3) 3x - 4y - 2z = -20
4x + y - z = 19
X - 2y + 3z = -23

A) Yes
B) No

Question 75

Determine whether the given point is in the solution set to the given system.
(2, 9, -4) 2x - 5y - 9z = -5
X + y + z = 7
3x - y + 5z = 35

A) No
B) Yes

Question 76

Determine whether the given point is in the solution set to the given system.
(5, -4, 5) 2x - 3y + 3z = 24
4x + 4y - 3z = -8
3x - 3y + 2z = 23

A) No
B) Yes

Question 77

Solve the system of equations.
x + 3y + 5z = 11 5y + 5z = 20
Z = 1

A) {(-3, 1, 3)}
B)
C) {(-3, 3, 1)}
D) {(1, 3, -3)}

Question 78

Solve the system of equations.
x - y + 2z = 10 2x + z = 4
X + 5y + z = -6

A)
B) {(0, -2, 4)}
C) {(4, -2, 0)}
D) {(4, 0, -2)}

Question 79

Solve the system of equations.
3x + 4y + z = -11 4x - 4y - z = -17
2x + y + 5z = 16

A)
B) {(-4, -1, 5)}
C) {(-4, 5, -1)}
D) {(5, -1, -4)}

Question 80

Solve the system of equations.
x - y + z = -7 x + y + z = 3
X + y - z = 9

A) {(1, -3, 5)}
B) {(-3, 1, 5)}
C)
D) {(1, 5, -3)}