Deck 8: Systems of Equations

Question 1

Solve graphically.
$$\begin{array} { l } 2 x + y = - 2 \\2 x + 2 y = 4\end{array}$$

A) $( 4,6 )$
В) $( - 4,6 )$
C) $( 2 , - 6 )$
D) $( - 4 , - 5 )$

Answer 1

B

Question 2

Classify the system as consistent or inconsistent, and dependent or independent.
$$\begin{array} { l } 2 x - 4 y = 2 \\y = \frac { 1 } { 2 } x - \frac { 1 } { 2 }\end{array}$$

A) Consistent and dependent
B) Consistent and independent
C) Inconsistent and dependent
D) Inconsistent and independent

Answer 2

A

Question 3

Classify the system as consistent or inconsistent, and dependent or independent.
$$\begin{array} { l } x + y = - 11 \\x - y = - 5\end{array}$$

A) Inconsistent and independent
B) Inconsistent and dependent
C) Consistent and dependent
D) Consistent and independent

Answer 3

D

Question 4

Solve graphically.
$$\begin{array} { l } 3 x + 4 y = 31 \\4 x - 2 y = 34\end{array}$$

A) No solution
B) $( 1,9 )$
C) $( 3,22 )$
D) $( 9,1 )$

Question 5

Solve graphically.
$$\begin{array} { l } \frac { 3 } { 2 } x - \frac { 1 } { 3 } y = 5 \\\frac { 5 } { 2 } x + \frac { 2 } { 3 } y = 12\end{array}$$

A) $( 4 , - 3 )$
В) $( 3,4 )$
C) $( 4,3 )$
D) $( 3,1 )$

Question 6

Classify the system as consistent or inconsistent, and dependent or independent.
$$\begin{array} { l } 3 x = y + 3 \\6 x - 2 y = 3\end{array}$$

A) Inconsistent and dependent
B) Consistent and independent
C) Inconsistent and independent
D) Consistent and dependent

Question 7

Classify the system as consistent or inconsistent, and dependent or independent.
$$\begin{array} { l } x - 8 = y \\y + 2 = x\end{array}$$

A) Inconsistent and independent
B) Consistent and independent
C) Consistent and dependent
D) Inconsistent and dependent

Question 8

Classify the system as consistent or inconsistent, and dependent or independent.
$$\begin{array} { c } x + 5 y = 19 \\5 x - 6 y = 2\end{array}$$

A) Inconsistent and independent
B) Consistent and independent
C) Consistent and dependent
D) Inconsistent and dependent

Question 9

Solve graphically.
$\begin{array}{l}2 x+y=6 \\4 x+2 y=12\end{array}$

A) No solution
B) Infinite number of solutions
C) $( 0,6 )$
D) $( 5 , - 4 )$

Question 10

Solve using the substitution method.
$$\begin{array} { l } x + y = 16 \\y = 3 x + 4\end{array}$$

A) $( 4,12 )$
B) $( 2,16 )$
C) $( 3,13 )$
D) $( 13,3 )$

Question 11

Solve graphically.
$\begin{array}{l}x=-y \\y+x=6\end{array}$

A) $( 1,5 )$
B) No solution
C) $( 1,1 )$
D) Infinite number of solutions

Question 12

Classify the system as consistent or inconsistent, and dependent or independent.
$$\begin{array} { c } - 10 x - 2 y = 10 \\5 x - y = - 5\end{array}$$

A) Consistent and independent
B) Inconsistent and independent
C) Inconsistent and dependent
D) Consistent and dependent

Question 13

Solve graphically.
$\begin{array}{c}3 x+2 y=5 \\-6 x-4 y=5\end{array}$

A) $( 1.5 , - 1 )$
B) No solution
C) $( 1,1 )$
D) $( - 1.5 , - 1 )$

Question 14

Classify the system as consistent or inconsistent, and dependent or independent.
$$\begin{array} { c } x + 6 y = 17 \\2 x + 12 y = 34\end{array}$$

A) Inconsistent and dependent
B) Consistent and dependent
C) Inconsistent and independent
D) Consistent and independent

Question 15

Solve using the substitution method.
$$\begin{array} { l } y = 2 x - 4 \\4 x + y = - 28\end{array}$$

A) $( - 5 , - 14 )$
В) $( - 12 , - 4 )$
C) $( - 12,20 )$
D) $( - 4 , - 12 )$

Question 16

Solve graphically.
$\begin{array}{c}3 x-2 y=4 \\-6 x+4 y=7\end{array}$

A) Infinite number of solutions
B) $( 2,1 )$
C) No solution
D) $( 1,2 )$

Question 17

Classify the system as consistent or inconsistent, and dependent or independent.
$$\begin{array} { l } 4 x + 4 y = 1 \\8 x + 8 y = 2\end{array}$$

A) Inconsistent and dependent
B) Consistent and dependent
C) Inconsistent and independent
D) Consistent and independent

Question 18

Classify the system as consistent or inconsistent, and dependent or independent.
$$\begin{array} { c } x + y = 8 \\2 x - 2 y = 8\end{array}$$

A) Inconsistent and dependent
B) Consistent and dependent
C) Consistent and independent
D) Inconsistent and independent

Question 19

Solve graphically.
$$\begin{array} { l } x = - 2 \\y = 1\end{array}$$

A) Infinitely many solutions
B) No solution
C) $( - 2,1 )$
D) $( 1 , - 2 )$

Question 20

Classify the system as consistent or inconsistent, and dependent or independent.
$$\begin{array} { r } x - 3 y = 6 \\3 y + 1 = x\end{array}$$

A) Consistent and independent
B) Inconsistent and independent
C) Consistent and dependent
D) Inconsistent and dependent

Question 21

Solve using the elimination method.
$x + y = 11$ $x - y = 7$

A) No solution
B) $( 9,2 )$
C) $( 8,3 )$
D) $( - 9,3 )$

Question 22

Solve by the substitution method.
$$\begin{array} { c } x + y = 7 \\5 x + 5 y = 35\end{array}$$

A) $( 0,0 )$
B) Infinite number of solutions
C) $( 7,5 )$
D) $( 8 , - 1 )$

Question 23

Solve by the substitution method.
$$\begin{array} { l } x - 5 y = - 27 \\- 6 x - 6 y = - 90\end{array}$$

A) No solution
В) $( - 8,8 )$
C) $( 7,8 )$
D) $( 8,7 )$

Question 24

Solve the problem.
The sum of two numbers is 34 and their difference is 12. Find the numbers.

A)23 and 11
B)25 and 37
C)9 and 25
D)11 and 23

Question 25

Solve by the substitution method.
$$\begin{array} { l } x + y = - 1 \\x + y = 4\end{array}$$

A) $( 0,3 )$
B) No solution
C) $( 0,0 )$
D) $( - 1,4 )$

Question 26

Solve by the substitution method.
$$\begin{array} { l } x + 6 y = - 1 \\7 x + 7 y = - 7\end{array}$$

A) $( - 1,0 )$
B) $( 0 , - 1 )$
C) $( 1 , - 1 )$
D) No solution

Question 27

Solve using the elimination method.
$$\begin{array} { l } 4 x - y = 19 \\5 x + y = 35\end{array}$$

A) $( 5,6 )$
B) $( 6,5 )$
C) $( 6,6 )$
D) No solution

Question 28

Solve the problem.
The perimeter of a rectangle is $78 \mathrm {~m}$ . If the width were doubled and the length were increased by $12 \mathrm {~m}$ , the perimeter would be $132 \mathrm {~m}$ . What are the length and width of the rectangle?

A) width $19 \mathrm {~m}$ , length $19 \mathrm {~m}$
B) width $14 \mathrm {~m}$ , length $19 \mathrm {~m}$
C) width $15 \mathrm {~m}$ , length $24 \mathrm {~m}$
D) width $24 \mathrm {~m}$ , length $15 \mathrm {~m}$

Question 29

Solve using the substitution method.
$$\begin{array} { l } x = 1 + - 2 y \\x + 2 y = 8\end{array}$$

A) Infinitely many solutions
B) $( - 7,15 )$
C) $( - 7 , - 15 )$
D) No solution

Question 30

Solve by the substitution method.
$$\begin{array} { l } 8 x + 8 y = - 32 \\5 x - 4 y = - 20\end{array}$$

A) $( - 5,1 )$
B) No solution
C) $( - 4,0 )$
D) $( - 4,1 )$

Question 31

Solve the problem.
Two angles have a sum of $81 ^ { \circ }$ . Their difference is $15 ^ { \circ }$ . Find the angles.

A) $67 ^ { \circ }$ and $14 ^ { \circ }$
B) $35 ^ { \circ }$ and $50 ^ { \circ }$
C) $48 ^ { \circ }$ and $33 ^ { \circ }$
D) $46 ^ { \circ }$ and $35 ^ { \circ }$

Question 32

Solve the problem.
The perimeter of a triangle is $65 \mathrm {~cm}$ . The triangle is isosceles now, but if its base were lengthened by $6 \mathrm {~cm}$ and each leg were shortened by $7 \mathrm {~cm}$ , it would be equilateral. Find the base of the original triangle.

A) $19 \mathrm {~cm}$
B) $26 \mathrm {~cm}$
C) $13 \mathrm {~cm}$
D) $12 \mathrm {~cm}$

Question 33

Solve the problem.
The perimeter of a rectangle is $56 \mathrm {~cm}$ . One side is $12 \mathrm {~cm}$ longer than the other side. Find the lengths of the sides.

A) $8 \mathrm {~cm} , 20 \mathrm {~cm}$
B) $11 \mathrm {~cm} , 23 \mathrm {~cm}$
C) $8 \mathrm {~cm} , 12 \mathrm {~cm}$
D) $16 \mathrm {~cm} , 28 \mathrm {~cm}$

Question 34

Solve by the substitution method.
$$\begin{array} { c } 7 x + 9 y = - 54 \\- 3 x - 4 y = 24\end{array}$$

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

Question 35

Solve by the substitution method.
$$\begin{array} { l } 6 x + 9 y = 114 \\4 x - 4 y = - 4\end{array}$$

A) No solution
B) $( 7,9 )$
C) $( 6,9 )$
D) $( 7,8 )$

Question 36

Solve by the substitution method.
$$\begin{array} { r } x + 3 y = 18 \\7 x + 4 y = 24\end{array}$$

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

Question 37

Solve the problem.
Find two numbers whose sum is 40 and whose difference is 12.

A)29 and 11
B)26 and 14
C)24 and 16
D)16 and 28

Question 38

Solve using the elimination method.
$$\begin{array} { l } - x - 3 y = - 2 \\- 5 x + 3 y = - 46\end{array}$$

A) $( 8 , - 2 )$
B) No solution
C) $( 9 , - 3 )$
D) $( 2,8 )$

Question 39

Solve the problem.
The sum of two angles is $225 ^ { \circ }$ . One angle is $30 ^ { \circ }$ less than twice the other. Find the angles.

A) $136 ^ { \circ }$ and $89 ^ { \circ }$
B) $85 ^ { \circ }$ and $140 ^ { \circ }$
C) $83 ^ { \circ }$ and $142 ^ { \circ }$
D) $83 ^ { \circ }$ and $136 ^ { \circ }$

Question 40

Solve by the substitution method.
$$\begin{array} { l } 8 x + 17 = 9 y \\- 6 x - 2 y = 4\end{array}$$

A) $( - 1,2 )$
B) No solution
C) $( - 2,2 )$
D) $( - 1,1 )$

Question 41

Solve the problem using the elimination method.
Two angles are supplementary, and one is $40 ^ { \circ }$ more than three times the other. Find the smaller angle.

A) $145 ^ { \circ }$
B) $105 ^ { \circ }$
C) $75 ^ { \circ }$
D) $35 ^ { \circ }$

Question 42

Solve the system of equations by the elimination method.
$$\begin{array} { l } \frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 18 \\\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 9\end{array}$$

A) $( - 12,0 )$
B) $( 0 , - 12 )$
C) $( 0,12 )$
D) $( 12,0 )$

Question 43

Solve the system of equations by the elimination method.
$$\begin{array} { c } x + 5 y = 2 \\- 4 x + 6 y = - 8\end{array}$$

A) $( 2,0 )$
B) no solution
C) $( 3,2 )$
D) $( - 2 , - 1 )$

Question 44

Solve the problem using the elimination method.
There were 490 people at a play. The admission price was $\$ 3$ for adults and $\$ 1$ for children. The admission receipts were $\$ 1070$ . How many adults and how many children attended?

A) 290 adults and 200 children
B) 267 adults and 223 children
C) 100 adults and 390 children
D) 200 adults and 290 children

Question 45

Solve the system of equations by the elimination method.
$$\begin{array} { l } 5 x - 6 y = - 5 \\15 x - 18 y = 15\end{array}$$

A) no solution
B) $( 25 , - 30 )$
C) infinitely many solutions
D) $( - 25,30 )$

Question 46

Solve the problem using the elimination method.
Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $\$ 81$ for 3 days and 300 miles, while Mary was charged $\$ 145$ for 5 days and 600 miles. What does Best Rental charge per day and per mile?

A) $\$ 18$ per day and $11 \nsubseteq$ per mile
B) $\$ 10$ per day and $17 \nsubseteq 5$ per mile
C) $\$ 16$ per day and $11 \nsubseteq \subset$ per mile
D) $\$ 17$ per day and $10 \simeq$ per mile

Question 47

Solve the system of equations by the elimination method.
$$\begin{array} { l } - 7 x - 6 y = - 36 \\- 3 x + 4 y = 24\end{array}$$

A) no solution
B) $( 0,7 )$
C) $( 0,6 )$
D) $( - 1,7 )$

Question 48

Solve the system of equations by the elimination method.
$$\begin{array} { r } 0.3 x + 0.5 y = 3.1 \\x - 0.1 y = 1.5\end{array}$$

A) $( 0.2,0.5 )$
B) $( 5,2 )$
C) no solution
D) $( 2,5 )$

Question 49

Solve the system of equations by the elimination method.
$$\begin{array} { c } x + 3 y = 15 \\- 6 x + 4 y = 20\end{array}$$

A) no solution
B) $( 1,4 )$
C) $( - 5,0 )$
D) $( 0,5 )$

Question 50

Solve using the elimination method.
$$\begin{array} { c } x + 6 y = 26 \\2 x + 6 y = 22\end{array}$$

A) $( 4,4 )$
B) No solution
C) $( - 4,5 )$
D) $( - 3 , - 4 )$

Question 51

Solve the system of equations by the elimination method.
$$\begin{array} { l } 3 x - 5 y = 2 \\18 x - 30 y = 12\end{array}$$

A) $( 6 , - 10 )$
B) infinitely many solutions
C) $( - 10,6 )$
D) no solution

Question 52

Solve the system of equations by the elimination method.
$$\begin{array} { l } 9 x + 9 y = - 45 \\- 4 x - 6 y = 20\end{array}$$

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

Question 53

Solve the problem using the elimination method.
A salesman sold $\$ 200$ more than the rest of the sales staff. If the sales total for the day was $\$ 2050$ , how much did the rest of the sales staff sell?

A) $\$ 1125$
B) $\$ 925$
C) $\$ 1850$
D) $\$ 1025$

Question 54

Solve the problem using the elimination method.
In a right triangle, one acute angle is $54 ^ { \circ }$ more than twice the other. Find each acute angle.

A) $12 ^ { \circ }$ and $78 ^ { \circ }$
B) $37 ^ { \circ }$ and $53 ^ { \circ }$
C) $21 ^ { \circ }$ and $69 ^ { \circ }$
D) $28 ^ { \circ }$ and $62 ^ { \circ }$

Question 55

Solve the system of equations by the elimination method.
$$\frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 21$$
$$\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 7$$

A) $( - 12,9 )$
В) $( 12,9 )$
C) $( - 12 , - 9 )$
D) $( 9 , - 12 )$

Question 56

Solve the problem using the elimination method.
There were 38,000 people at a ball game in Los Angeles. The day's receipts were $\$ 229,000$ . How many people paid $\$ 11$ for reserved seats and how many paid $\$ 4$ for general admission?

A) 19,250 paid $\$ 11$ and 18,750 paid $\$ 4$
B) 27,000 paid $\$ 11$ and 11,000 paid $\$ 4$
C) 18,750 paid $\$ 11$ and 19,250 paid $\$ 4$
D) 11,000 paid $\$ 11$ and 27,000 paid $\$ 4$

Question 57

Solve the problem using the elimination method.
Two angles are supplementary, and one is $5 ^ { \circ }$ more than six times the other. Find the larger angle.

A) $25 ^ { \circ }$
B) $155 ^ { \circ }$
C) $70 ^ { \circ }$
D) $110 ^ { \circ }$

Question 58

Solve the system of equations by the elimination method.
$- 0.8 x + 0.4 y = 4.8$ $0.1 x - 0.1 y = - 0.7$

A) $( - 50,20 )$
В) $( - 0.5,0.2 )$
C) $( - 5,2 )$
D) $( 2 , - 5 )$

Question 59

Solve the system of equations by the elimination method.
$$\begin{array} { l } 2.5 x + 0.3 y = 10.6 \\0.5 x + 0.9 y = 3.8\end{array}$$

A) $( 6.5,2.3 )$
B) $( 4,2 )$
C) $( 4.5,2 )$
D) $( 1.5,2.3 )$

Question 60

Solve the system of equations by the elimination method.
$$\begin{array} { c } x - 3 y = - 5 \\4 x - 4 y = 12\end{array}$$
$4 \mathrm { x } - 4 \mathrm { y } = 12$

A) $( 7,4 )$
В) $( 6,5 )$
C) no solution
D) $( - 7,5 )$

Question 61

Solve the problem using the elimination method.
The sum of two numbers is 100 . The second number is three times as large as the first number. What are the numbers?

A) 22 and 78
B) 23 and 69
C) 23 and 77
D) 25 and 75

Question 62

Solve the problem.
A merchant has coffee worth $\$ 20$ a pound that she wishes to mix with 90 pounds of coffee worth $\$ 90$ a pound to get a mixture that can be sold for $\$ 80$ a pound. How many pounds of the $\$ 20$ coffee should be used?

A) $7.5 \mathrm { lb }$
B) $52.5 \mathrm { lb }$
C) $105 \mathrm { lb }$
D) $15 \mathrm { lb }$

Question 63

Solve the problem.
There were 670 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $1020. How many adults and how many children attended?

A)320 adults and 350 children
B)255 adults and 415 children
C)350 adults and 320 children
D)160 adults and 510 children

Question 64

Solve the problem.
Anne and Nancy use a metal alloy that is $16 \%$ copper to make jewelry. How many ounces of an alloy that is $10 \%$ copper must be mixed with an alloy that is $20 \%$ copper to form 55 ounces of the desired alloy?

A) 22 ounces
B) 33 ounces
C) 38 ounces
D) 24 ounces

Question 65

Solve the problem.
Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 28 coins with a total face value of $\$ 5.00$ , how many of the coins are nickels?

A) 23 nickels
B) 10 nickels
C) 12 nickels
D) 18 nickels

Question 66

Solve the problem.
Walt made an extra $\$ 10,000$ last year from a part-time job. He invested part of the money at $10 \%$ and the rest at $9 \%$ . He made a total of $\$ 960$ in interest. How much was invested at $9 \%$ ?

A) $\$ 8000$
B) $\$ 5000$
C) $\$ 6000$
D) $\$ 4000$

Question 67

Solve the problem.
Andy has 33 coins made up of quarters and half dollars, and their total value is $\$ 13.25$ . How many quarters does he have?

A) 18 quarters
B) 22 quarters
C) 20 quarters
D) 13 quarters

Question 68

Solve the problem.
Ellen wishes to mix candy worth $\$ 1.79$ per pound with candy worth $\$ 3.75$ per pound to form 22 pounds of a mixture worth $\$ 2.95$ per pound. How many pounds of the more expensive candy should she use?

A) 13 pounds
B) 11 pounds
C) 9 pounds
D) 18 pounds

Question 69

Solve the problem.
Mardi received an inheritance of $\$ 60,000$ . She invested part at $8 \%$ and deposited the remainder in tax-free bonds at $11 \%$ . Her total annual income from the investments was $\$ 5700$ . Find the amount invested at $8 \%$ .

A) $\$ 54,300$
B) $\$ 29,000$
C) $\$ 30,000$
D) $\$ 15,000$

Question 70

Solve the problem.
A sum of money amounting to $\$ 3.45$ consists of dimes and quarters. If there are 18 coins in all, how many are quarters?

A) 16 quarters
B) 7 quarters
C) 11 quarters
D) 9 quarters

Question 71

Solve the problem.
How many liters of a $20 \%$ alcohol solution must be mixed with 90 liters of a $80 \%$ solution to get a $40 \%$ solution?

A) $27 \mathrm {~L}$
B) $18 \mathrm {~L}$
C) $180 \mathrm {~L}$
D) $270 \mathrm {~L}$

Question 72

Solve the problem using the elimination method.
The sum of two numbers is 41 . The larger number minus the smaller number is 9 . What are the numbers?

A) 18 and 27
B) 25 and 16
C) 33 and 8
D) 23 and 18

Question 73

Solve the problem.
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 28 pounds of feed worth $\$ 0.62$ per pound by mixing one kind worth $\$ 0.15$ per pound with another worth $\$ 0.97$ per pound. How many pounds of the cheaper kind should they use in the mix?

A) 21 pounds
B) 14 pounds
C) 12 pounds
D) 16 pounds

Question 74

Solve the problem.
A woman made a deposit of $267. If her deposit consisted of 91 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

A)44 one-dollars
B)42 one-dollars
C)37 one-dollars
D)47 one-dollars

Question 75

Solve the problem.
In a chemistry class, 6 liters of a $4 \%$ silver iodide solution must be mixed with a $10 \%$ solution to get a $6 \%$ solution. How many liters of the $10 \%$ solution are needed?

A) $4.0 \mathrm {~L}$
B) $3.0 \mathrm {~L}$
C) $2.0 \mathrm {~L}$
D) $6.0 \mathrm {~L}$

Question 76

Solve the problem using the elimination method.
In a basketball game, Will scored 40 points, consisting only of three-point shots and two-point shots. He made a total of 17 shots. How many shots of each type did he make?

A) two-point shots: 11 ; three-point shots: 6
B) two-point shots: 6; three-point shots: 11
C) two-point shots: 10 ; three-point shots: 7
D) two-point shots: 12; three-point shots: 5

Question 77

Solve the problem using the elimination method.
A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $\$ 5.00$ . Another customer buys 4 hot dogs and 3 bags of potato chips for $\$ 9.00$ . Find the cost of each item.

A) $\$ 1.75$ for a hot dog; $\$ 1.25$ for a bag of potato chips
B) $\$ 1.50$ for a hot dog; $\$ 1.25$ for a bag of potato chips
C) $\$ 1.00$ for a hot dog; $\$ 1.50$ for a bag of potato chips
D) $\$ 1.50$ for a hot dog; $\$ 1.00$ for a bag of potato chips

Question 78

Solve the problem.
A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with $9 \%$ cement should he mix with 10 bags of $10.8 \%$ cement to produce a mix containing $10 \%$ cement?

A) 23 bags
B) 10 bags
C) 8 bags
D) 18 bags

Question 79

Solve the problem.
Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $3.00 each and Kathy selling adult tickets for $5.50 each. If their total income for 25 tickets was $120.00, how many did Ron sell?

A)23 tickets
B)18 tickets
C)7 tickets
D)9 tickets

Question 80

Solve the problem using the elimination method.
The sum of two numbers is 4 . Three times the larger number plus two times the smaller number is 37 . Find the numbers.

A) 25 and $- 21$
B) 33 and $- 29$
C) 29 and $- 25$
D) 25 and $- 29$