Deck 6: Systems of Equations

Question 1

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $$\begin{array} { r } x - 2 y = 7 \\2 x + 3 y = 0\end{array}$$

A) (4, -2)
B) (3, -2)
C) (5, -2)
D) (3, -3)
E) (3, -1)

Answer 1

(3, -2)

Question 2

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $$\begin{array} { l } 2 x + y = 4 \\2 y + x = 4\end{array}$$

A) yes
B) no
C) insufficient information

Answer 2

no

Question 3

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $$\begin{array} { c } 5 x - 3 y = 11 \\- 20 x + 12 y = - 44\end{array}$$

A) (5, -3)
B) (3, 5)
C) (-5, -4)
D) (-4, 3)
E) any (x, y) on line $5 x - 3 y = 11$

Answer 3

any (x, y) on line $5 x - 3 y = 11$

Question 4

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) $$\begin{array} { l } y = 4 x \\y = \frac { 1 } { 4 } ( 12 + 20 x )\end{array}$$

A) yes
B) no
C) insufficient information

Question 5

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $$\begin{array} { l } y + x = 30 \\2 x = 60 - 2 y\end{array}$$

A) yes
B) no
C) insufficient information

Question 6

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $$\begin{array} { l } y = x + 0.04 x \\y = 1.04 x\end{array}$$

A) yes
B) no
C) insufficient information

Question 7

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $$\begin{array} { l } y + 100 x = 400 \\y = 100 - 400 x\end{array}$$

A) yes
B) no
C) insufficient information

Question 8

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Paolo earns $481 from working 54 total hours at two jobs. He earns $6.55 per hour (x) at the first job and $9.20 per hour (y) at the second job.

A) $x = 54 + y , 6.55 x + 9.20 y = 481$
B) $x + y = 54,9.20 x + 6.55 y = 481$
C) $x + y = 54,6.55 x + 9.20 y = 481$
D) $x + y = 54,6.55 x - 9.20 y = 481$
E) $x - y = 54,655 x + 9.20 y = 481$

Question 9

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Martina has 58 nickels and dimes. She has $3.10 altogether. She has x nickels and y dimes.

A) y = 58 - x, 0.05x + 0.10y = 3.10
B) x + y = 58, 0.05y + 0.10x = 3.10
C) $x + y = 58,0.25 x + 0.10 y = 3.10$
D) x - y = 58, 0.05x + 0.10y = 3.10
E) $x - y = 58,0.05 y + 0.25 x = 3.10$

Question 10

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Ed works on two projects during one month. He works 28 hours longer on one project (y) than on the other (x). He works a total of 186 hours during the month.

A) x + y = 186, x = y + 28
B) x - y = 186, x = y + 28
C) x + y = 186, x = y - 28
D) y - x = 186, y = x - 28
E) x - y = 186, x = y - 28

Question 11

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Jacques cuts a 14-decimeter submarine sandwich into two pieces. One piece (y) is 2 decimeters longer than the other (x).

A) x + y = 14, x = y + 2
B) x + y = 14, x = y - 2
C) x - y = 14, x = y + 2
D) y - x = 14, y = x - 2
E) y - x = 14, x = y - 2

Question 12

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $$\begin{aligned}4 x - y & = 14 \\2 x - 3 y & = 12\end{aligned}$$

A) (4, -1)
B) (2, -2)
C) (3, -2)
D) (3, -3)
E) (4, -2)

Question 13

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Alexandra works for two clients during one month. She works a total of 180 hours during the month. She works 50 hours more for one client (y) than for the other (x).

A) x + y = 180, x = y + 50
B) x - y = 180, x = y + 50
C) y - x = 180, y = x - 50
D) $x + y = 180 , y = x + 50$
E) x + y = 180, x - y = 50

Question 14

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Nancy has $3.50. She has only dimes (x) and quarters (y). She has 30 coins altogether.

A) x = 30 - y, 0.10x + 0.25y = 3.50
B) $x - y = 30,0.10 x + 0.25 y = 3.50$
C) y - x = 30, 0.10x + 0.25y = 3.50
D) x + y = 30, 0.05x + 0.25y = 3.50
E) $x + y = 30,0.05 y + 0.25 x = 3.50$

Question 15

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $$\begin{array} { l } y - 2.8 x = 3.8 \\0.6 x + y = 0.4\end{array}$$

A) (-1, 2)
B) (0, 1)
C) (-1, 0)
D) (-1, 1)
E) (0, 2)

Question 16

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Renee cuts a 12-meter hose into two lengths. One piece (x) is 2 meters longer than the other (y). What is the length of each piece?

A) $x + y = 12 , x = y + 2$
B) $x + y = 12 , y = x + 2$
C) x - y = 12, x = y + 2
D) y - x = 12, y = x - 2
E) x + y = 12, x = y - 2

Question 17

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) $$\begin{array} { l } 2 x + 2 y = 40 \\y = 30 - x\end{array}$$

A) yes
B) no
C) insufficient information

Question 18

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) $$\begin{array} { l } y = 9 - x \\y = 2 + x\end{array}$$

A) yes
B) no
C) insufficient information

Question 19

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Larry has 26 nickels and quarters. He has $2.20 altogether. He has x nickels and y quarters.

A) x - y = 26, 0.10y + 0.25x = 2.20
B) x + y = 26, 0.10x + 0.25y = 2.20
C) x - y = 26, 0.05x + 0.25y = 2.20
D) x + y = 26, 0.05y + 0.25x = 2.20
E) x = 26 - y, 0.05x + 0.25y = 2.20

Question 20

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $$\begin{array} { r } x - 2 y = 5 \\5 x - 10 y = 3\end{array}$$

A) (2, 5)
B) (2, 10)
C) (5, 10)
D) (5, 5)
E) no solution

Question 21

Decide which variable has a coefficient of 1 or -1, and solve for that variable in terms of the other variable. $4 x + y = 3$

A) $y = - 3 - 4 x$
B) $y = 3 - 4 x$
C) $y = 4 x + 3$
D) $y = 3 x - 4$
E) $y = 4 x - 3$

Question 22

Decide which variable has a coefficient of 1 or -1, and solve for that variable in terms of the other variable. $2 y - x = 7$

A) $x = 2 y + 7$
B) $x = 7 y + 2$
C) $x = 7 y - 2$
D) $x = 2 y - 7$
E) $x = 7 - 2 y$

Question 23

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. Tickets for five students and two adults to a Saturday morning magic show cost $25. Tickets for six students and one adult cost $26.50. Find the price of an adult ticket.

A) Adult ticket is $5.00.
B) Adult ticket is $2.50.
C) Adult ticket is $3.00.
D) Adult ticket is $4.00.
E) Adult ticket is $3.50.

Question 24

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. An airplane flies westbound from Denver to San Francisco (950 miles) with the wind in 3.8 hours. On a return flight against the same wind, the travel time is 5 hours. Find the speed of the wind, w.

A) w = 45 mph
B) w = 40 mph
C) w = 35 mph
D) w = 30 mph
E) w = 25 mph

Question 25

Find the rate of travel for a fishing boat with a speed of 10 miles per hour (mph) moving downstream with a current of 5 mph.

A) 15 mph
B) 10 mph
C) 7.5 mph
D) 5 mph
E) -5 mph

Question 26

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. A boat travels 20 miles downstream in an hour. While its passengers are fishing, the tide comes in. The tidewater reaches 20 miles upstream. The trip home on still water take 1 $\frac { 1 } { 4 }$ hours. Find the speed of the current, c.

A) c = 1.5 mph
B) c = 2.0 mph
C) c = 2.5 mph
D) c = 3.0 mph
E) c = 4.0 mph

Question 27

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. Two of the top-price tickets and five of the lowest-price tickets for a Tim McGraw concert cost $660. Three of the top-price and three of the lowest-price tickets cost $900. Find the cost of the top-price ticket.

A) Top-price ticket costs $270.
B) Top-price ticket costs $105.
C) Top-price ticket costs $230.
D) Top-price ticket costs $280.
E) Top-price ticket costs $250.

Question 28

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Restaurants buy 10-pound and 25-pound bags of carrots. They want five times as many 10-pound bags (x) as 25-pound bags (y). If the company estimates that restaurants will buy 450 pounds of carrots, how many bags of each size should be packaged?

A) $y = 5 x , 10 x + 25 y = 450$
B) $x = 5 y , 10 y - 25 x = 450$
C) $x = 5 y , x + y = 450$
D) $y = 5 x , x + y = 450$
E) $x = 5 y , 10 x + 25 y = 450$

Question 29

Decide which variable has a coefficient of 1 or -1, and solve for that variable in terms of the other variable. $4 x - y = 17$

A) $y = 4 x + 17$
B) $y = 17 x + 4$
C) $y = 17 x - 4$
D) $y = 17 - 4 x$
E) $y = 4 x - 17$

Question 30

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. An airplane flies eastbound from Boise to Chicago, covering the 1400 miles with the wind in 4 hours. A return flight against the same wind takes 5 hours. Find the speed of the wind, w.

A) w = 30 mph
B) w = 35 mph
C) w = 40 mph
D) w = 25 mph
E) w = 20 mph

Question 31

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. The I.R.Rabbit Company sells carrots. It sells six times as many pounds to grocery stores as to restaurants. It has 5,300 pounds of carrots. The company sells x pounds of carrots to grocery stores and y pounds of carrots to restaurants.

A) $x + y = 5,300 , y = 6 x$
B) $x - y = 5,300 , x = 6 y$
C) $y - x = 5,300 , x = 6 y$
D) $x + y = 5,300 , x = 6 y$
E) $x = 5,300 + y , y = 6 x$

Question 32

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. Two of the top-price tickets and eight of the lowest-price tickets for a Norah Jones concert cost $2,391. Three of the top-price and four of the lowest-price tickets cost $2,946.50. Find the cost of the top-price ticket.

A) Top-price ticket costs $731.50
B) Top-price ticket costs $675.50
C) Top-price ticket costs $835.50
D) Top-price ticket costs $915.50
E) Top-price ticket costs $875.50

Question 33

Solve 10 = m(4) + b for m.

A) $2.5 - \frac { b } { 4 } = m$
B) $\frac { 10 } { 4 } - b = m$
C) $10 - \frac { b } { 4 } = m$
D) 40 - 4b = m
E) 2.5 - b = m

Question 34

Decide which variable has a coefficient of 1 or -1, and solve for that variable in terms of the other variable. $5 x + y = 25$

A) $y = 25 + 5 x$
B) $y = 25 x + 5$
C) $y = 25 - 5 x$
D) $y = 25 x - 5$
E) $y = 5 x - 25$

Question 35

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. On a weekend, two adult movie tickets and three student tickets cost $36.50. Three adult and two student tickets cost $38.50. Find the price of the adult ticket.

A) Adult ticket is $8.50.
B) Adult ticket is $6.50.
C) Adult ticket is $7.50.
D) Adult ticket is $9.50.
E) Adult ticket is $4.50.

Question 36

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. A boat travels 12 miles upstream to a fishing spot. The trip takes 1.2 hours. The return trip, downstream, takes 0.8 hour. Find the speed of the current, c.

A) c = 2.0 mph
B) c = 2.5 mph
C) c = 2.8 mph
D) c = 3.0 mph
E) c = 3.5 mph

Question 37

Solve D = rt for r.

A) $\frac { D } { r } = t$
B) D - r = t
C) D - t = r
D) Dt = r
E) $\frac { D } { t } = r$

Question 38

Solve for x. $6 = - 3 x - 12 ( - 2 )$

A) $x = 6$
B) $x = - 10$
C) $x = 8$
D) $x = - 6$
E) $x = 10$

Question 39

Solve by substitution: $$\begin{aligned}y & = 3 x + 13 \\x + 5 y & = - 15\end{aligned}$$

A) (-5, -2)
B) (-4, 1)
C) (-6, -5)
D) Dependent
E) No solution

Question 40

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. Three adult and five university student tickets for the alternative music hall cost $86.50. Five adult and eight student tickets cost $141. Find the price of an adult ticket.

A) Adult ticket is $8.50.
B) Adult ticket is $12.
C) Adult ticket is $13.
D) Adult ticket is $9.50.
E) Adult ticket is $15.

Question 41

Solve by substitution: $$\begin{array} { l } 5 x - 5 y = - 5 \\4 x + 2 y = 20\end{array}$$

A) (13, 14)
B) (8, 9)
C) (3, 4)
D) Dependent
E) No solution

Question 42

The sum of two numbers is 37. Their difference is 6. Identify two appropriate variables, and use the variables to write equations. Use either the elimination method or substitution method to solve the equations.

A) Twice the larger number is 41.
B) Twice the larger number is 43.
C) Twice the larger number is 42.
D) Twice the smaller number is 30.
E) Twice the smaller number is 29.

Question 43

To cut costs, the new manager at Healthy Options wants to mix 4,000 pounds of cat food. The mixture is to have 10% protein. The first ingredient contains 8% protein. The second has 13% protein. How many pounds of the 8% protein ingredient is needed?

A) 1,200 pounds of 8%
B) 2,400 pounds of 8%
C) 1,360 pounds of 8%
D) 1,880 pounds of 8%
E) 1,500 pounds of 8%

Question 44

Solve by the elimination method: $$\begin{array} { l } 10 x + 39 y = 16 \\15 x + 39 y = 18\end{array}$$

A) $\left( \frac { 1 } { 3 } , \frac { 4 } { 13 } \right)$
B) $\left( \frac { 2 } { 5 } , \frac { 4 } { 13 } \right)$
C) $\left( \frac { 2 } { 5 } , \frac { 1 } { 3 } \right)$
D) $\left( \frac { 1 } { 3 } , \frac { 1 } { 3 } \right)$
E) No solution

Question 45

Solve by substitution: $$\begin{aligned}y & = - 4 - 4 x \\16 x + 4 y & = - 16\end{aligned}$$

A) (3, -16)
B) (4, -20)
C) (2, -12)
D) Dependent, $y = - 4 - 4 x$
E) No solution

Question 46

Define variables for the measures of angles. Write equations based on the given facts as well as the characteristics of complementary angles and supplementary angles. Solve the given resulting system of equations by elimination.
a) Two angles are complementary. The measure of one angle is $30 ^ { \circ }$ larger than that of the other.
b) Two angles are supplementary. The measure of one angle is $30 ^ { \circ }$ larger than that of the other.

A) a) $55,35$
b) $100,80$
B) a) $60,30$
b) $100,80$
C) a) $60,30$
b) $105,75$
D) a) $50,40$
b) $95,85$
E) a) $55,35$
b) $95,85$

Question 47

Identify two appropriate variables, and use the variables to write equations. Use either the elimination method or the substitution method to solve the equation The sum of two numbers is $40$ _. There difference is $6$ .
Find the numbers.

A) $23.5,16.5$
B) $23,17$
C) $18,12$
D) $25,15$
E) $26,14$

Question 48

Solve by the elimination method: $$\begin{array} { l } 2 x - 4 y = 6 \\5 x + 5 y = - 15\end{array}$$

A) (-5, -4)
B) (3, 0)
C) (-1, -2)
D) Dependent
E) No solution

Question 49

A parallelogram has angles A and B as supplementary angles. The measure of angle A is 74 degrees more than angle B. What is the measure of angle A?

A) A = 53 degrees
B) A = 67 degrees
C) A = 82 degrees
D) A = 127 degrees
E) A = 113 degrees

Question 50

Two DVDs and three game disks cost $137.79. Four DVDs and one game disk cost $75.73. What does one of each cost?

A) DVD = $9.09, game disk = $39.87
B) DVD = $11.88, game disk = $40.09
C) DVD = $9.15, game disk = $39.83
D) DVD = $8.94, game disk = $39.97
E) DVD = $9.00, game disk = $39.93

Question 51

Solve by substitution: $$\begin{aligned}y & = 12 - 4 x \\4 x + y & = 14\end{aligned}$$

A) (3, 0)
B) (4, -4)
C) (2, 4)
D) Dependent
E) No solution

Question 52

The perimeter of the front of a 20-ounce Cheerios box is 44 inches. The height is 4 inches more than the width. What is the width of the box?

A) width = 13 inches
B) width = 10 inches
C) width = 14 inches
D) width = 11 inches
E) width = 9 inches

Question 53

Solve by the elimination method: $$\begin{array} { l } 5 x + 5 y = 30 \\2 x + 2 y = 3\end{array}$$

A) (5, 1)
B) (-10, 16)
C) (0, 6)
D) (-5, 11)
E) No solution

Question 54

Solve by the elimination method: $$\begin{array} { l } 4 x - 4 y = 4 \\4 x + 2 y = 4\end{array}$$

A) (5, 4)
B) (1, 0)
C) (9, 8)
D) Dependent
E) No solution

Question 55

Yoko has $5.00 in quarters and nickels. She has 24 coins altogether. How many quarters does she have?

A) 19 quarters
B) 5 quarters
C) 20 quarters
D) 4 quarters
E) 21 quarters

Question 56

At the bookstore, 2 notebooks and 5 pens cost $14.69. At the same time, 6 notebooks and 3 pens cost $32.67. What is the cost of one of each?

A) notebooks = $4.87, pens = $0.99
B) notebooks = $4.92, pens = $0.97
C) notebooks = $4.97, pens = $0.95
D) notebooks = $4.79, pens = $1.31
E) notebooks = $4.77, pens = $1.03

Question 57

Shrimp is 24.3% protein (by weight), and cooked brown rice is 2.9% protein (by weight). A mixture weighing 1113 grams is made from the shrimp and brown rice. The mixture needs to contain 63 grams of protein. How many grams of shrimp are to be used? Round to the nearest gram.

A) 969 grams of shrimp
B) 144 grams of shrimp
C) 139 grams of shrimp
D) 134 grams of shrimp

Question 58

A right triangle has angles A and B as complementary angles. The measure of angle A is 8 more than the measure of angle B. What is the measure of angle A?

A) A = 94 degrees
B) A = 86 degrees
C) A = 41 degrees
D) A = 53 degrees
E) A = 49 degrees

Question 59

Solve by the elimination method: $$\begin{array} { r } 9 x - 3 y = 6 \\12 x - 4 y = 8\end{array}$$

A) (0, -2)
B) (-9, -29)
C) (-3, -11)
D) (-6, -20)
E) Dependent. The solutions satisfy the equation $3 x - y = 2$

Question 60

Two angles are complementary. The measure of one angle is 60 degrees less than that of the other. Define variables for the measures of the angles. Write equations based on the given facts. Solve the resulting system by elimination to find the measures of the angles.

A) 30 degrees, 60 degrees
B) 60 degrees, 120 degrees
C) 15 degrees, 75 degrees
D) 20 degrees, 80 degrees
E) 150 degrees, 210 degrees

Question 61

In the graph of y $\leq$ 0, x $\geq$ -1 what is the corner point?

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

Question 62

In the graph of x $\geq$ 3, y $\leq$ -2, what is the corner point?

A) (-2, -3)
B) (-3, 2)
C) (3, -2)
D) (-3, -2)
E) (-2, 3)

Question 63

Nerine combines walking (at 6 km/hr) and running (at 18 km/hr) in her fitness program. Last week she exercised a total of 10 hours and traveled 108 kilometers. How many hours did she walk?

A) 5 hours
B) 6 hours
C) 4 hours
D) 8 hours
E) 2 hours

Question 64

In the graph of y $\geq$ 1, x $\leq$ 0 what is the corner point?

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

Question 65

Which ordered pairs satisfy the system of inequalities given? $$\begin{array} { l } x + y > 1 \\x - y > 1\end{array}$$

A) $( 7,0 )$
B) $( 0,0 )$
C) $( 2,2 )$
D) $( 0,7 )$
E) $( 7,7 )$

Question 66

Graph the system of Inequalities and show the solutions set. Label the corner point. $$\begin{array} { l } x > - 1 \\y \leq 3\end{array}$$

A)
B)
C)
D)
E)

Question 67

Which ordered pairs satisfy the system of inequalities given? $$\begin{array} { l } x + y < 5 \\x + y > - 5\end{array}$$

A) $( 0,0 )$
B) $( 1,5 )$
C) $( 2,2 )$
D) $( 6,6 )$
E) $( 1 , - 6 )$

Question 68

In the graph of x < 1, y $\geq$ -2, what is the corner point?

A) (1, 2)
B) (1, -2)
C) (-2, 1)
D) (-2, -1)
E) (0, -2)

Question 69

Graph the system of Inequalities and show the solution set. Label the corner point. $$\begin{array} { l } y \geq 3 x - 4 \\y > - x + 4\end{array}$$

A)
B)
C)
D)
E)

Question 70

Graph the system of Inequalities and show the solution set. Label the corner point. $$\begin{array} { l } y > 5 x - 5 \\y < 2 x - 2\end{array}$$

A)
B)
C)
D)
E)

Question 71

Which ordered pairs satisfy the system of inequalities given? $$\begin{array} { l } y \leq - x - 4 \\y \geq x\end{array}$$

A) $( 0,0 )$
B) $( 0 , - 1 )$
C) $( - 4,4 )$
D) $( - 4 , - 4 )$
E) $( - 6 , - 6 )$

Question 72

Graph the system of inequalities and show the solution set. $$\left\{ \begin{array} { l } y \leq - x - 1 \\y \geq 2 x - 2\end{array} \right.$$

A)
B)
C)
D)
E)

Question 73

Which ordered pairs satisfy the system of inequalities given? $$\begin{array} { l } y \leq x + 4 \\y \geq x - 4\end{array}$$

A) $( 1,1 )$
B) $( 1 , - 4 )$
C) $( - 5,5 )$
D) $( - 6,6 )$
E) $( 1 , - 6 )$