Deck 4: Systems of Linear Equations

Question 1

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$$\left\{ \begin{array} { l } \frac { 1 } { 2 } x - y = 1 \\x = 2\end{array} \right.$$

A) $\{ ( 2,0 ) \}$
B) $\left\{ \left( 2 , \frac { 1 } { 2 } \right) \right\}$
C) $\{ ( 2,1 ) \}$
D) $\{ ( 0,2 ) \}$

Answer 1

$\{ ( 2,0 ) \}$

Question 2

Determine whether the ordered pair is a solution of the system.
$$\begin{array} { l } ( - 2 , - 2 ) \\\left\{ \begin{array} { l } 2 x + y = - 2 \\3 x + 2 y = - 2\end{array} \right.\end{array}$$

A) Yes
B) No

Answer 2

No

Question 3

Determine whether the ordered pair is a solution of the system.
$$\begin{array} { l } ( 3 , - 1 ) \\\left\{ \begin{array} { l } x + y = - 4 \\x - y = - 2\end{array} \right.\end{array}$$

A) Yes
B) No

Answer 3

No

Question 4

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$$\left\{ \begin{array} { l } 4 x + 4 y = 36 \\2 x - 2 y = 2\end{array} \right.$$

A) $\{ ( 5,4 ) \}$
B) no solution; $\varnothing$
C) $\{ ( 4 , - 6 ) \}$
D) $\{ ( 4,5 ) \}$

Question 5

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$$\left\{ \begin{array} { l } 3 x + y = - 11 \\4 x + 2 y = - 12\end{array} \right.$$

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

Question 6

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$\left\{\begin{array}{l}x-3 y=-3 \\2 x+3 y=12\end{array}\right.$

A) $\{ ( 2,3 ) \}$
B) no solution; $\varnothing$
C) $\{ ( 3,2 ) \}$
D) $\{ ( 3 , - 2 ) \}$

Question 7

Determine whether the ordered pair is a solution of the system.
$$\begin{array} { l } ( - 1 , - 6 ) \\\left\{ \begin{array} { l } 2 x + y = - 8 \\3 x + 2 y = - 15\end{array} \right.\end{array}$$

A) Yes
B) No

Question 8

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$\left\{\begin{array}{l}3 x+y=-7 \\2 x+y=-6\end{array}\right.$

A) no solution; $\varnothing$
B) $\{ ( - 1 , - 4 ) \}$
C) $\{ ( 1,4 ) \}$
D) $\{ ( - 4 , - 1 ) \}$

Question 9

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$\left\{\begin{array}{l}x=-y \\y+x=6\end{array}\right.$

A) $\{ ( 1,5 ) \}$
B) $\{ ( 1,1 ) \}$
C) no solution; $\varnothing$
D) infinitely many solutions; $\{ ( x , y ) \mid y + x = 6 \}$ or $\{ ( x , y ) \mid x = - y \}$

Question 10

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$$\left\{ \begin{array} { l } x + \frac { 3 } { 4 } y = - 8 \\x = - 5\end{array} \right.$$

A) $\{ ( - 5 , - 4 ) \}$
B) $\{ ( - 5,4 ) \}$
C) no solution; $\varnothing$
D) $\{ ( 5 , - 4 ) \}$

Question 11

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$$\left\{ \begin{array} { l } 2 x - y = - 8 \\y = 2\end{array} \right.$$

A) $\{ ( - 3,2 ) \}$
B) no solution; $\varnothing$
C) $\{ ( 3 , - 2 ) \}$
D) $\{ ( 2 , - 3 ) \}$

Question 12

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$\left\{\begin{array}{l}y-4 x=2 \\6 y=24 x+12\end{array}\right.$

A) $\{ ( 1,1 ) \}$
B) no solution; $\varnothing$
C) $\{ ( - 1.5 , - 1 ) \}$
D) infinitely many solutions; $\{ ( x , y ) \mid y - 4 x = 2 \}$ or $\{ ( x , y ) \mid 6 y = 24 x + 12 \}$

Question 13

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$\left\{\begin{array}{l}y=x+3 \\y=3 x+7\end{array}\right.$

A) $\{ ( - 2,1 ) \}$
B) $\{ ( 2 , - 1 ) \}$
C) $\{ ( 1 , - 2 ) \}$
D) no solution; $\varnothing$

Question 14

Determine whether the ordered pair is a solution of the system.
(4, -2) $$\left\{ \begin{array} { l } 2 x = 6 - y \\3 x = 8 - 2 y\end{array} \right.$$

A) Yes
B) No

Question 15

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$\left\{\begin{array}{l}4 x+y=12 \\16 x+4 y=48\end{array}\right.$

A) no solution; $\varnothing$
B) $\{ ( 0,12 ) \}$
C) $\{ ( 5 , - 8 ) \}$
D) infinitely many solutions; $\{ ( x , y ) \mid 4 x + y = 12 \}$ or $\{ ( x , y ) \mid 16 x + 4 y = 48 \}$

Question 16

Determine whether the ordered pair is a solution of the system.
(-2, -1) $$\left\{ \begin{array} { l } 2 \mathrm { x } = 3 - \mathrm { y } \\4 \mathrm { x } = 6 - 2 \mathrm { y }\end{array} \right.$$

A) Yes
B) No

Question 17

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$\left\{\begin{array}{l}5 x+y=-16 \\2 x+3 y=4\end{array}\right.$

A) $\{ ( - 4,4 ) \}$
B) $\{ ( - 3 , - 1 ) \}$
C) $\{ ( - 4 , - 5 ) \}$
D) $\{ ( 4,4 ) \}$

Question 18

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$\left\{\begin{array}{l}y=x+6 \\y=-3 x-2\end{array}\right.$

A) $\{ ( - 2 , - 4 ) \}$
B) $\{ ( - 4 , - 2 ) \}$
C) no solution; $\varnothing$
D) $\{ ( - 2,4 ) \}$

Question 19

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$$\left\{ \begin{array} { l } x = 7 \\y = - 3\end{array} \right.$$

A) infinitely many solutions; $\{ ( x , y ) \mid x = 7 \}$ or $\{ ( x , y ) \mid y = - 3 \}$
B) $\{ ( - 3,7 ) \}$
C) $\{ ( 7 , - 3 ) \}$
D) no solution; $\varnothing$

Question 20

Determine whether the ordered pair is a solution of the system.
$$\begin{array} { l } ( 3 , - 1 ) \\\left\{ \begin{array} { l } x + y = 2 \\x - y = 4\end{array} \right.\end{array}$$

A) Yes
B) No

Question 21

Solve the problem.
$$\left\{ \begin{array} { l } - 2 x - 6 y = - 3 \\4 x + 12 y = 0\end{array} \right.$$

A) $\{ ( - 3,0 ) \}$
B) no solution; $\varnothing$
C) infinitely many solutions; $\{ ( x , y ) \mid 4 x + 12 y = 0 \}$ or $\{ ( x , y ) \mid - 2 x - 6 y = - 3 \}$
D) $\{ ( 0 , - 3 ) \}$

Question 22

Solve the problem.
$$\left\{ \begin{array} { l } x - 6 = y \\y + 8 = x\end{array} \right.$$

A) no solution; $\varnothing$
B) $\{ ( 8,6 ) \}$
C) $\{ ( 6,8 ) \}$
D) infinitely many solutions; $\{ ( x , y ) \mid x - 6 = y \}$ or $\{ ( x , y ) \mid y + 8 = x \}$

Question 23

Solve the problem.
$$\left\{ \begin{array} { l } - 7 x + 9 y = - 21 \\- 4 x - 2 y = - 12\end{array} \right.$$

A) $\{ ( 2,1 ) \}$
B) $\{ ( 3,0 ) \}$
C) no solution; $\varnothing$
D) $\{ ( 3,1 ) \}$

Question 24

Solve the problem.
$$\left\{ \begin{array} { r } x - 2 y = 16 \\- 2 x - 3 y = 3\end{array} \right.$$

A) no solution; $\varnothing$
B) $\{ ( 6 , - 5 ) \}$
C) $\{ ( 5 , - 4 ) \}$
D) $\{ ( - 6 , - 4 ) \}$

Question 25

Solve the problem.
$$\left\{ \begin{array} { l } y - 6 x = 4 \\4 y = 24 x + 16 \\\text { A) } \{ ( - 1.5 , - 1 )\end{array} \right.$$

A) $\{ ( - 1.5 , - 1 ) \}$
B) no solution; $\varnothing$
C) $\{ ( 1,1 ) \}$
D) infinitely many solutions; $\{ ( x , y ) \mid y - 6 x = 4 \}$ or $\{ ( x , y ) \mid 4 y = 24 x + 16 \}$

Question 26

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$$\left\{ \begin{array} { l } 2 x + y = 3 \\2 x + y = 2\end{array} \right.$$

A) no solution; $\varnothing$
B) $\left\{ \left[ \frac { 3 } { 2 } , 0 \right) \right\}$
C) infinitely many solutions; $\{ ( x , y ) \mid 2 x + y = 3 \}$ or $\{ ( x , y ) \mid 2 x + y = 2 \}$
D) $\{ ( 1,0 ) \}$

Question 27

Solve the problem.
$$\left\{ \begin{array} { l } \frac { 1 } { 2 } x + \frac { 1 } { 2 } y = - 1 \\x - y = 4\end{array} \right.$$

A) $\{ ( 0 , - 2 ) \}$
B) no solution; $\varnothing$
C) $\{ ( 1 , - 3 ) \}$
D) $\{ ( - 1 , - 2 ) \}$

Question 28

Solve the problem.
$$\left\{ \begin{array} { c } 3 x + y = 14 \\12 x + 4 y = 56\end{array} \right.$$

A) no solution; $\varnothing$
B) $\{ ( 0,14 ) \}$
C) $\{ ( 5 , - 1 ) \}$
D) infinitely many solutions; $\{ ( x , y ) \mid 3 x + y = 14 \}$ or $\{ ( x , y ) \mid 12 x + 4 y = 56 \}$

Question 29

Solve the problem.
$$\left\{ \begin{array} { l } x + y = - 4 \\y = 3 x\end{array} \right.$$

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

Question 30

Solve the problem.
$$\left\{ \begin{array} { l } x = - y \\x + y = 6\end{array} \right.$$

A) $\{ ( 1,5 ) \}$
B) no solution; $\varnothing$
C) infinitely many solutions; $\{ ( x , y ) \mid x + y = 6 \}$ or $\{ ( x , y ) \mid x = - y \}$
D) $\{ ( 1,1 ) \}$

Question 31

Solve the problem.
$$\left\{ \begin{array} { l } y = 2 x + 4 \\4 x + y = - 8\end{array} \right.$$

A) $\{ ( 0 , - 2 ) \}$
B) $\{ ( - 3 , - 2 ) \}$
C) $\{ ( - 2,0 ) \}$
D) $\{ ( 0 , - 8 ) \}$

Question 32

Solve the problem.
$$\left\{ \begin{array} { r } x - 7 y = - 1 \\2 x - 6 y = - 2\end{array} \right.$$

A) $\{ ( 1 , - 1 ) \}$
B) $\{ ( 0 , - 1 ) \}$
C) no solution; $\varnothing$
D) $\{ ( - 1,0 ) \}$

Question 33

Solve the problem.
$$\left\{ \begin{array} { l } y = 1.4 x - 3.7 \\y = 0.8 x - 3.04\end{array} \right.$$

A) $\{ ( - 1.1 , - 2.16 ) \}$
B) infinitely many solutions; $\{ ( x , y ) \mid y = 1.4 x - 3.7 \}$ or $\{ ( x , y ) \mid y = 0.8 x - 3.04 \}$
C) no solution; $\varnothing$
D) $\{ ( 1.1 , - 2.16 ) \}$

Question 34

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$$\left\{ \begin{array} { l } y = 0 \\y = - 5\end{array} \right.$$

A) $\{ ( - 5,0 ) \}$
B) $\{ ( 0 , - 5 ) \}$
C) no solution; $\varnothing$
D) infinitely many solutions; $\{ ( x , y ) \mid y = - 5 \}$ or $\{ ( x , y ) \mid y = 0 \}$

Question 35

Solve the problem.
$$\left\{ \begin{array} { l } y = 5 x + 4 \\y = 8 x + 3\end{array} \right.$$

A) infinitely many solutions; $\{ ( x , y ) \mid y = 5 x + 4 \}$ or $\{ ( x , y ) \mid y = 8 x + 3 \}$
B) no solution; $\varnothing$
C) $\left\{ \left( \frac { 17 } { 3 } , \frac { 1 } { 3 } \right) \right\}$
D) $\left\{ \left( \frac { 1 } { 3 } , \frac { 17 } { 3 } \right) \right\}$

Question 36

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
$\left\{\begin{array}{l}x=8 \\x=-5\end{array}\right.$

A) no solution; $\varnothing$
B) $\{ ( - 5,8 ) \}$
C) infinitely many solutions; $\{ ( x , y ) \mid x = 8 \}$ or $\{ ( x , y ) \mid x = - 5 \}$
D) $\{ ( 8 , - 5 ) \}$

Question 37

Solve the problem.
$$\left\{ \begin{array} { l } 9 x + 4 y = 20 \\- 2 x - 2 y = - 10\end{array} \right.$$

A) $\{ ( - 1,6 ) \}$
B) no solution; $\varnothing$
C) $\{ ( 0,6 ) \}$
D) $\{ ( 0,5 ) \}$

Question 38

Solve the problem.
$$\left\{ \begin{array} { l } 9 x + 8 y = 12 \\- 4 x - 2 y = - 10\end{array} \right.$$

A) no solution; $\varnothing$
B) $\{ ( 4 , - 2 ) \}$
C) $\{ ( 3 , - 2 ) \}$
D) $\{ ( 4 , - 3 ) \}$

Question 39

Solve the problem.
$$\left\{ \begin{array} { l } x + y = - 9 \\x - y = 19\end{array} \right.$$

A) $\{ ( 5 , - 14 ) \}$
B) $\{ ( 5,14 ) \}$
C) $\{ ( 9,5 ) \}$
D) $\{ ( 9 , - 14 ) \}$

Question 40

Solve the problem.
$$\left\{ \begin{array} { r } x + 2 y = 2 \\9 x + 3 y = 3\end{array} \right.$$

A) $\{ ( 1,0 ) \}$
B) no solution; $\varnothing$
C) $\{ ( 0,1 ) \}$
D) $\{ ( - 1,0 ) \}$

Question 41

Solve the problem.
A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 3 bags of potato chips for $5.25. Another customer buys 4 hot dogs and 4 bags of potato chips for $9.00. Find the cost of each item.

A) $1.50 for a hot dog; $0.75 for a bag of potato chips
B) $0.75 for a hot dog; $1.50 for a bag of potato chips
C) $1.50 for a hot dog; $1.00 for a bag of potato chips
D) $1.75 for a hot dog; $1.00 for a bag of potato chips

Question 42

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } x + y = 7 \\x - y = 1\end{array} \right.$$

A) $\{ ( 3,4 ) \}$
B) $\{ ( - 4,4 ) \}$
C) no solution; $\varnothing$
D) $\{ ( 4,3 ) \}$

Question 43

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } 3 x + \frac { 1 } { 4 } y = - 7 \\5 x + \frac { 1 } { 3 } y = - \frac { 34 } { 3 }\end{array} \right.$$

A) $\{ ( - 1 , - 5 ) \}$
B) no solution; $\varnothing$
C) $\{ ( 2 , - 5 ) \}$
D) $\{ ( - 2 , - 4 ) \}$

Question 44

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { c } x + 4 y = - 17 \\2 x + 4 y = - 18\end{array} \right.$$

A) $\{ ( 0 , - 1 ) \}$
B) $\{ ( 1 , - 5 ) \}$
C) no solution; $\varnothing$
D) $\{ ( - 1 , - 4 ) \}$

Question 45

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } 8 x - 3 y = 1 \\8 x - 3 y = 5\end{array} \right.$$

A) no solution; $\varnothing$
B) $\left\{ \left( \frac { 1 } { 3 } , \frac { 5 } { 8 } \right) \right\}$
C) $\{ ( 1,5 ) \}$
D) $\{ ( 8,3 ) \}$

Question 46

Solve the problem.
An electronics company kept comparative statistics on two products, A and B. For the years 2003 to 2011, the total number of Product A ever sold (in thousands) is given by the equation y = 77x + 200, where x is the
Number of years since 2003. For that same period, the total number of Product B ever sold (in thousands) is
Given by the equation y = -30x + 434, where x is the number of years since 2003. Use the substitution method to
Solve the system and choose the statement that most accurately describes the solution.

A) At about 2.2 years (to the nearest tenth) since 2003, the company sold the same number of Product A as Product B.
B) At some point between 2003 and 2011, the company had sold 2200 of each product.
C) When 369,000 of Product A had been sold, 2.2 times as many of Product B had been sold.
D) The company sold about 2.2 times as many of Product B as Product A.

Question 47

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } 2 x - 5 y = 5 \\3 x - 4 y = 5\end{array} \right.$$

A) no solution; $\varnothing$
B) infinitely many solutions; $\{ ( x , y ) \mid 2 x - 5 y = 5 \}$ or $\{ ( x , y ) \mid 3 x - 4 y = 5 \}$
C) $\left\{ \left( \frac { 5 } { 7 } , - \frac { 5 } { 7 } \right) \right\}$
D) $\left\{ \left( - \frac { 5 } { 7 } , \frac { 5 } { 7 } \right) \right\}$

Question 48

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { r } x + 4 y = 36 \\8 x + 5 y = 45\end{array} \right.$$

A) $\{ ( 0,9 ) \}$
B) $\{ ( 1,8 ) \}$
C) no solution; $\varnothing$
D) $\{ ( - 9,0 ) \}$

Question 49

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

A) 6 and 11
B) -10 and -5
C) 5 and 10
D) 4 and 9

Question 50

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } 9 x + 5 y = 51 \\7 x - 2 y = 75\end{array} \right.$$

A) no solution; $\varnothing$
B) $\{ ( 9 , - 6 ) \}$
C) $\{ ( 9 , - 5 ) \}$
D) $\{ ( 8 , - 5 ) \}$

Question 51

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { c } x + 8 y = 15 \\- 2 x + 7 y = - 7\end{array} \right.$$

A) $\{ ( 6,2 ) \}$
B) $\{ ( - 7,2 ) \}$
C) $\{ ( 7,1 ) \}$
D) no solution; $\varnothing$

Question 52

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } 6 x - 12 = 6 y \\2 x + 2 y = - 20\end{array} \right.$$

A) $\{ ( - 4 , - 5 ) \}$
B) no solution; $\varnothing$
C) $\{ ( - 5 , - 5 ) \}$
D) $\{ ( - 4 , - 6 ) \}$

Question 53

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { r } x + 7 y = 68 \\3 x + 7 y = 78\end{array} \right.$$

A) $\{ ( 6,8 ) \}$
B) no solution; $\varnothing$
C) $\{ ( - 9,5 ) \}$
D) $\{ ( 5,9 ) \}$

Question 54

Solve the problem.
One number is 2 less than a second number. Twice the second number is 40 more than 5 times the first. Find the two numbers.

A) -11 and -9
B) 10 and 12
C) -12 and -10
D) -13 and -11

Question 55

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } 2 x + 10 y = - 64 \\9 x + 2 y = 56\end{array} \right.$$

A) $\{ ( -2 , 8 ) \}$
B) $\{ ( 9 , - 9 ) \}$
C) $\{ ( 8 , - 8 ) \}$
D) $\{ ( - 8,8 ) \}$

Question 56

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } \frac { 1 } { 3 } x + \frac { 1 } { 3 } y = 1 \\\frac { 1 } { 4 } x - \frac { 1 } { 4 } y = - \frac { 9 } { 4 }\end{array} \right.$$

A) $\{ ( 3,7 ) \}$
B) $\{ ( - 3,6 ) \}$
C) $\{ ( - 4,7 ) \}$
D) no solution; $\varnothing$

Question 57

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } x + y = 8 \\x + y = 4\end{array} \right.$$

A) $\{ ( 8,4 ) \}$
B) no solution; $\varnothing$
C) $\{ ( 0,0 ) \}$
D) $\{ ( 0,12 ) \}$

Question 58

Solve the problem.
A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 4 soft drinks for $34.72. The second group bought 5 slices of pizza and 5 soft drinks for $
26)50. How much does one slice of pizza cost?

A) $2.42 per slice of pizza
B) $2.88 per slice of pizza
C) $3.38 per slice of pizza
D) $1.92 per slice of pizza

Question 59

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } 7 x + 5 y = - 20 \\3 x + 3 y = - 12\end{array} \right.$$

A) $\{ ( - 1 , - 3 ) \}$
B) $\{ ( 0 , - 3 ) \}$
C) no solution; $\varnothing$
D) $\{ ( 0 , - 4 ) \}$

Question 60

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } \frac { x + 5 } { 3 } = \frac { y + 19 } { 6 } \\\frac { x } { 2 } = \frac { 2 y + 8 } { 4 }\end{array} \right.$$

A) $\{ ( 1,5 ) \}$
B) no solution; $\varnothing$
C) $\{ ( 5,1 ) \}$
D) infinitely many solutions; $\left\{ ( x , y ) \mid \frac { x + 5 } { 3 } = \frac { y + 19 } { 6 } \right\}$ or $\left\{ ( x , y ) \mid \frac { x } { 2 } = \frac { 2 y + 8 } { 4 } \right\}$

Question 61

Solve the system by the best method. Use set notation to express the solution set.
$$\left\{ \begin{array} { l } - 2 x - 8 y = - 38 \\6 x - 9 y = - 18\end{array} \right.$$

A) $\{ ( - 3,5 ) \}$
B) $\{ ( 3,4 ) \}$
C) $\{ ( 2,5 ) \}$
D) no solution; $\varnothing$

Question 62

Solve the system by the best method. Use set notation to express the solution set.
$$\left\{ \begin{array} { c } x + 8 y = - 61 \\8 x + 7 y = - 89\end{array} \right.$$

A) no solution; $\varnothing$
B) $\{ ( - 5 , - 7 ) \}$
C) $\{ ( 5 , - 6 ) \}$
D) $\{ ( - 6 , - 6 ) \}$

Question 63

Solve the system by the best method. Use set notation to express the solution set.
\(\left\{ \begin{array} { r } 4 x = - 4 - 8 y \\ 2 x - 5 y = 34 \\ \text { \end{array} \right.\)

A)\(\{ ( 6 , - 3 ) \}\)
B) \(\{ ( 7 , - 3 ) \}\)
C) \(\{ ( 7 , - 4 ) \}\)
D) no solution; \(\varnothing\)

Question 64

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } 4 x = 8 y + 9 \\4 x = 8 y - 4\end{array} \right.$$

A) $\left\{ \left( \frac { 1 } { 8 } , \frac { 1 } { 16 } \right) \right\}$
B) no solution; $\varnothing$
C) $\left\{ \left( 0 , - \frac { 9 } { 8 } \right) \right\}$
D) $\{ ( 8,9 ) \}$

Question 65

Solve the system by the best method. Use set notation to express the solution set.
$$\left\{ \begin{array} { l } 8 x + 98 = 6 y \\- 3 x - 4 y = - 7\end{array} \right.$$

A) $\{ ( - 8,8 ) \}$
B) no solution; $\varnothing$
C) $\{ ( - 7,8 ) \}$
D) $\{ ( - 7,7 ) \}$

Question 66

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } 7 x - 2 y = 6 \\- 21 x + 6 y = - 24\end{array} \right.$$

A) $\{ ( 7,6 ) \}$
B) $\{ ( 3,4 ) \}$
C) no solution; $\varnothing$
D) $\left\{ \left( \frac { 7 } { 9 } , - \frac { 2 } { 9 } \right) \right\}$

Question 67

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } 8 x - 2 y = 10 \\24 x - 6 y = 50\end{array} \right.$$

A) $\{ ( 10,50 ) \}$
B) $\{ ( 3,5 ) \}$
C) no solution; $\varnothing$
D) $\left\{ \left( \frac { 15 } { 8 } , - \frac { 15 } { 2 } \right) \right\}$

Question 68

Solve the problem.
On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $11 each and a number of necklaces at $14 each. She wrote a check for $1590 to pay for the order. How many bracelets
And how many necklaces did Rosaria purchase?

A) 35 bracelets and 85 necklaces
B) 25 bracelets and 95 necklaces
C) 40 bracelets and 80 necklaces
D) 30 bracelets and 90 necklaces

Question 69

Solve the system by the best method. Use set notation to express the solution set.
$$\left\{ \begin{array} { l } y = 3 x + 5 \\4 x + y = 33\end{array} \right.$$

A) $\{ ( 3,14 ) \}$
B) $\{ ( 17 , - 35 ) \}$
C) $\{ ( 4,17 ) \}$
D) $\{ ( 17,4 ) \}$

Question 70

Solve the problem.
One number is four more than a second number. Two times the first number is 12 more than four times the second number.

A) 1 and - 3
B) 3 and - 1
C) - 10 and - 14
D) 2 and - 2

Question 71

Solve the system by the best method. Use set notation to express the solution set.
$$\left\{ \begin{array} { l } 3 x = - 9 \\x + 5 y = 17\end{array} \right.$$

A) $\{ ( 3,4 ) \}$
B) no solution; $\varnothing$
C) $\{ ( 3 , - 4 ) \}$
D) $\{ ( - 3,4 ) \}$

Question 72

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
$$\left\{ \begin{array} { l } - 5 x + 4 y = - 6 \\8 y = - 12 + 10 x\end{array} \right.$$

A) $\{ ( 0,0 ) \}$
B) $\{ ( - 5,4 ) \}$
C) no solution; $\varnothing$
D) infinitely many solutions; $\{ ( x , y ) \mid - 5 x + 4 y = - 6 \}$ or $\{ ( x , y ) \mid 8 y = - 12 + 10 x \}$

Question 73

Solve the system by the best method. Use set notation to express the solution set.
$$\left\{ \begin{array} { l } 5 x + 6 y = 8 \\5 x + 6 y = 11\end{array} \right.$$

A) $\{ ( 6,5 ) \}$
B) $\{ ( 5,6 ) \}$
C) $\{ ( 1,1 ) \}$
D) no solution; $\varnothing$

Question 74

Solve the system by the best method. Use set notation to express the solution set.
$$\left\{ \begin{array} { l } x + y = 6 \\y = 2 x\end{array} \right.$$

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

Question 75

Solve the problem.
Two numbers total 12, and their difference is 16. Find the two numbers.

A) 7 and 5
B) 6 and - 10
C) 12 and 2
D) 14 and - 2

Question 76

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
\(\left\{ \begin{array} { c } 4 x + y = 12 \\ 16 x + 4 y = 48 \\ \text { \end{array} \right.\)

A) \(\{ ( 5 , - 8 ) \}\)
B) infinitely many solutions; \(\{ ( x , y ) \mid 4 x + y = 12 \}\) or \(\{ ( x , y ) \mid 16 x + 4 y = 48 \}\)
C) no solution; \(\varnothing\)
D) \(\{ ( 0,12 ) \}\)

Question 77

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 5 times as many dimes as nickels, and the value of the dimes is $2.70 more
Than the value of the nickels. How many nickels and dimes does Jamil have?

A) 7 nickels and 35 dimes
B) 5 nickels and 25 dimes
C) 6 nickels and 30 dimes
D) 30 nickels and 6 dimes

Question 78

Solve the problem.
The sum of two numbers is -5. Three times the first number equals 2 times the second number. Find the two numbers.

A) -10 and -15
B) - 2 and - 3
C) 2 and 3
D) -5 and 6

Question 79

Solve the system by the best method. Use set notation to express the solution set.
$$\left\{ \begin{array} { l } x + 8 y = 0 \\x - 8 y = 32\end{array} \right.$$

A) $\{ ( 8 , - 1 ) \}$
B) $\{ ( 16 , - 2 ) \}$
C) $\{ ( 16,2 ) \}$
D) $\{ ( - 2,16 ) \}$

Question 80

Solve the problem.
Devon purchased tickets to an air show for 8 adults and 2 children. The total cost was $218. The cost of a child's ticket was $6 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: $22; child's ticket: $16
B) adult's ticket: $25; child's ticket: $19
C) adult's ticket: $23; child's ticket: $17
D) adult's ticket: $24; child's ticket: $18