Deck 42: Two Variable Linear Systems

Question 1

Solve the system of linear equations by the method of elimination.Use the graph to check your solution.​ ​​

A)(-2,2)
B)​ (-2,6) ​
C)(2,-2)​​
D)​(2,-6)​
E)​(-2,-6)

Answer 1

(2,-2)​​

Question 2

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. ​​ ​

A)(-1,0)​ ​
​
B)​(0,1) ​
​
C)(10,1) ​
​
D)​(1,10)​
E)​(1,0) ​
​

Answer 2

(-1,0)​ ​
​

Question 3

Solve the system of linear equations by the method of elimination.Use the graph to check your solution.​ ​

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

Answer 3

​(1,1)

Question 4

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ ​

A)​(1,4)
B)​(4,1)
C)(-​4,-1)
D)(​4,-1)
E)​(1,-4)

Question 5

Find the equilibrium point (x,p)of the demand and supply equations.The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations. ​
Demand
Supply ​

A)​(-500,-115)
B)​​(500,115)
C)​​(-500,115)
D)​(115,-500)
E)​​(115,500)

Question 6

​Use any method to solve the system of linear equations,find (x,y).​ ​

A)​(-10,-5)
B)(10,-5)
C)​(3,-5)
D)​​(-5,10)
E)​​​(-5,-10)

Question 7

Use any method to solve the system of linear equations,find (x,y).​ ​

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

Question 8

​Use any method to solve the system of linear equations,find (x,y).​ ​ ​

A)​(3,4)
B)​(4,-3)
C)​​(-3,-4)
D)​​(-3,4)
E)​​(4,-3)

Question 9

​Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically. ​​ ​

A)​(2,-2)
B)​(2,2)
C)​(2,9)
D)​(-2,-2)
E)​(-2,2)

Question 10

Use any method to solve the system of linear equations,find (x,y).​ ​

A)​​​(1,-2)
B)​​(1,2)
C)​(7,2)
D)​(-2,1)
E)(2,1)

Question 11

Find the equilibrium point (x,p)of the demand and supply equations.The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations. ​
Demand
Supply ​

A)​(290,300,000)
B)​(290,-300,000) ​
C)(-300,000,-290) ​
D)(300,000,290)
E)(-300,000,290) ​

Question 12

Use any method to solve the system of linear equations,find (x,y). ​​ ​

A)​(145,19)
B)​​(-19,145)
C)​(19,-145)
D)​​(145,-19)
E)​​(-145,19)

Question 13

Find the equilibrium point (x,p)of the demand and supply equations.The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations. ​
Demand
Supply ​

A)(250,445)​
B)​​(445,-250)​
C)​(445,250)​
D)​(-250,445)​
E)​(-250,-445)​

Question 14

Two cheeseburgers and one small order of French fries from a fast-food restaurant contain a total of 850 calories.Three cheeseburgers and two small orders of French fries contain a total of 1380 calories.Find the caloric content of each item. ​

A)Cheeseburger: 320 calories;French fries: 210 calories
B)​Cheeseburger: 210 calories;French fries: 320 calories
C)​Cheeseburger: 850 calories;French fries: 320 calories
D)​Cheeseburger: 210 calories;French fries: 210 calories
E)​Cheeseburger: 320 calories;French fries: 320 calories

Question 15

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. ​​ ​​

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

Question 16

One eight-ounce glass of apple juice and one eight-ounce glass of orange juice contain a total of 176.4 milligrams of vitamin C.Twoeight-ounce glasses of apple juice and three eight-ounce glasses of orange juice contain a total of 432.7 milligrams of vitamin C.How much vitamin C is in an eight-ounce glass of each type of juice? ​

A)​Apple juice: 96.5 mg;Orange juice: 96.5 mg
B)Apple juice: 96.5 mg;Orange juice: 79.9 mg
C)​Apple juice: 79.9 mg;Orange juice: 79.9 mg
D)​Apple juice: 79.9 mg;Orange juice: 96.5 mg
E)​Apple juice: 176.4 mg;Orange juice: 79.9 mg

Question 17

Find the equilibrium point (x,p)of the demand and supply equations.The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations. ​
Demand
Supply ​

A)(103,1,250,000)
B)​(-1,250,000,-103)
C)​(1,250,000,103)
D)​(103,-1,250,000)
E)​(-1,250,000,103)

Question 18

Fourty liters of a 40% acid solution is obtained by mixing a 28% solution with a 50% solution.Write a system of equations in which one equation represents the amount of final mixture required and the other represents the percent of acid in the final mixture.Let x and y represent the amounts of the 28% and 50% solutions,respectively. ​

A)​
B)​
C)
D)​
E)​

Question 19

Solve the system of linear equations by the method of elimination.Use the graph to check your solution.​ ​

A)​(2,2)​ ​
B)​(2,9)​ ​
C)​(-9,9)​ ​
D)​(9,- 2)​ ​
E)No solution​ ​

Question 20

Solve the system of linear equations by the method of elimination.Use the graph to check your solution.​ ​​

A)(9,2)​ ​
B)​(- 4,2) ​ ​
​
C)​(2,- 9) ​
D)​(- 2,- 4) ​
E)No solution ​

Question 21

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ ​

A)(97,107)
B)(107,97)
C)(107,-97) ​
D)(-97,107) ​
E)(-107,97) ​

Question 22

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ ​

A)​
B)
C)​
D)​
E)​

Question 23

Seven hundred gallons of 87-octane gasoline is obtained by mixing 87-octane gasoline with 90-octane gasoline.Use a graphing utility to graph the two given equations.Let x and y represent the number of gallons of the 87-octane gasoline and 90-octane gasoline.As the number of gallons of the 87-octane gasoline increases,how does the number of gallons of the 90-octane gasoline change?​ ​

A)​ Increases
B)​ Decreases
C)​ Decreases
D)​ Increases
E)​ Decreases

Question 24

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically. ​​ ​

A)​(14,13)
B)(-14,-13) ​
C)(-14,14)
D)(-14,13)
E)(14,-13)

Question 25

Use any method to solve the system of linear equations,find (x,y). ​​ ​

A)(7,4)
B)​(4,7)
C)​​(4,-7)
D)​(-7,4)
E)​(-7,-4)

Question 26

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ ​

A)​
B)​
C)​
D)​
E)

Question 27

​Solve the system of linear equations by the method of elimination,find (x,y).​ ​ ​

A)No solution
B)​
C)​
D)​
E)​

Question 28

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 29

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ ​

A)​(18,6)
B)(-18,-6) ​
C)(-18,18)
D)(-18,6)
E)​(18,-6) ​

Question 30

Sixty liters of a 43% acid solution is obtained by mixing a 28% solution with a 42% solution.Use a graphing utility to graph the two given equations.Let x and y represent the amounts of the 28 % solution and 42% solution.As the amount of the 28% solution increases,how does the amount of the 42% solution change? ​ ​
​

A)​ ​
Increases
B)​ ​
Decreases
C)​ ​
Decreases
D)​ ​
Decreases
E)​
Increases

Question 31

Solve the system by the method of elimination and check any solutions algebraically. ​​ ​

A)(4,- 3)
B)(4,3)
C)​(7,- 7)
D)​(- 4,3)
E)​(- 4,- 3)

Question 32

Solve the system of linear equations by the method of elimination.Find (r,s)and check your solution algebraically.​ ​

A)​
B)​
C)​
D)​
E)​

Question 33

A total of $23,000 is invested in two corporate bonds that pay 3.5% and 5% simple interest.The investor wants an annual interest income of $880 from the investments.What amount should be invested in the 3.5% bond? ​

A)$22,800
B)$18,000
C)$23,000
D)$18,300
E)$18,100

Question 34

A total of $32,000 is invested in two municipal bonds that pay 5.75% and 6.25% simple interest.The investor wants an annual interest income of $1,900 from the investments.What amount should be invested in the 5.75% bond? ​

A)$31,800
B)$20,000
C)$32,000
D)$20,300
E)$20,100

Question 35

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ ​

A)
B)​
C)​
D)​
E)​

Question 36

Thirty​ liters of a 40% acid solution is obtained by mixing a 28% solution with a 43% solution.How much of each solution is required to obtain the specified concentration of the final mixture? Use this system of linear equations there x and y represents the amounts of the 28% solution and 43% solution. ​​ ​

A)​28% solution: 6 L;43% solution: 24 L
B)43% solution: 6 L;28% solution: 24 L​
C)​28% solution: 40 L;43% solution: 24 L
D)​43% solution: 40 L;28% solution: 24 L
E)​43% solution: 7 L;28% solution: 24 L

Question 37

​Seven hundred gallons of 89-octane gasoline is obtained by mixing 87-octane gasoline with 92-octane gasoline.How much of each type of gasoline is required to obtain the 700 gallons of 89-octane gasoline? Use this system of linear equations there x and y represent the number of gallons of the 87-octane gasoline and 89-octane gasoline. ​​ ​

A)87​-octane: 89 gal;92-octane: 280 gal ​
B)87​-octane: 280 gal;92-octane: 420 gal​
C)92​​-octane: 89 gal;87-octane: 280 gal
D)​​87-octane: 420 gal;92-octane: 280 gal
E)​​92-octane: 280 gal;87-octane: 89 gal

Question 38

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ ​

A)(4,1)
B)(4,-4) ​
C)(-4,-1) ​
D)(4,-1) ​
E)(-4,1) ​

Question 39

Seven hundred gallons of 91-octane gasoline is obtained by mixing 87-octane gasoline with 94-octane gasoline.Write a system of equations in which one equation represents the amount of final mixture required and the other represents the amounts of 87- and 94-octane gasolines in the final mixture.Let x and y represent the numbers of gallons of 87-octane and 94-octane gasolines,respectively. ​

A)​
B)​
C)​
D)​
E)​

Question 40

Solve the system of linear equations by the method of elimination.Find (u,v)and check your solution algebraically.​ ​

A)​
B) ​
C) ​
D) ​
E) ​

Question 41

​Solve the system of linear equations by the method of elimination,find (x,y). ​​ ​

A)​
B)
C)​
D)No solution
E)​

Question 42

An airplane flying into a headwind travels 1128.00 miles in 4 hours and 42 minutes.On the return flight,the distance is traveled in 4 hours.Find the airspeed of the plane and the speed of the wind,assuming that both remain constant. ​

A)plane speed = 238 mph;wind speed = 250 mph
B)plane speed = 276 mph;wind speed = 21.00 mph
C)plane speed = 261.00 mph;wind speed = 21.00 mph
D)plane speed = 238 mph;wind speed = 21.00 mph
E)plane speed = 276 mph;wind speed = 268 mph

Question 43

​Solve the system of linear equations by the method of elimination,find (x,y). ​​ ​

A)​(4,-43)
B)(a,-7 - 9a)​(infinitely many solutions)
C)​(2,-25)
D)​No solutions
E)​(8,-79)

Question 44

​Solve the system of linear equations using any method,find (x,y). ​​ ​

A)​
B)​
C)​No solution
D)​
E)​

Question 45

Find the equilibrium point (x,p)of the demand and supply equations.(The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations. ) Demand
Supply
P = 129.00 - 0.07x
P = 0.2x - 60
​

A)​(200,115)
B)(700,80)
C)No solution
D)​(514,42.8)
E)(300,108)​

Question 46

A wildlife biologist has spent the past 5 years studying the relationship between the length (inches)and the average weight (lb)of the striped bass.His results are summarized in the table below.
Find the least squares regression line y = ax + b for the data in the table,where x represents the length of the fish in inches and y represents the weight in pounds.Use this regression line to estimate the average weight of a striped bass that is 21 inches in length.

A)y = 0.85(21)- 12.5 = 5.35 lb
B)y = 0.95(21)- 10.5 = 9.45 lb
C)y = 0.95(21)- 8.5 = 11.45 lb
D)y = 0.75(21)- 9.5 = 6.25 lb
E)y = 0.65(21)- 10.5 = 3.15 lb

Question 47

Solve the system of linear equations by the method of elimination,find (x,y). ​​ ​

A)No solution
B)​(20 + 9a,a)(infinitely many solutions)
C)(-3,-7)
D)(38,2)
E)(-7,-3)

Question 48

​Solve the system of linear equations using any method,find (x,y). ​​ ​

A)​
B)​
C)​
D)No solution
E)​

Question 49

During one performance of a local arts council's presentation of Fiddler on the Roof,the box office sold 225 tickets and collected $1638.If adult tickets sold for $9 and children's tickets sold for $6,how many of each type of ticket were sold? ​

A)adult tickets sold = 96;children's tickets sold = 129
B)adult tickets sold = 115;children's tickets sold = 148
C)adult tickets sold = 129;children's tickets sold = 96
D)adult tickets sold = 115;children's tickets sold = 100
E)adult tickets sold = 148;children's tickets sold = 115