Name: ____________________________________ Date: ____________________

1B L86: TOPICAL REVIEW #2 – SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES

1. If , then x equals 1) 2) 3)

4)

2. If , what is x expressed in terms of a and b?

3. What is the value of x in the equation ?

1) 2) 16 3) 4) 4

4. Solve for x:

5. Solve the following system of equations. 4 3 17

3 2 13

x y

x y

+ =

+ =

6. Which of the following is the value of y that solves the system of equations shown below? (1) 5− (3) 6 (2) 8 (4) 2− 7. Find the value of x that solves the system shown below. Show the work that leads to your answer.

2

3

y x

x y

= −

+ =

8. Which of the following values of x solves the system shown below? (1) 5x = − (3) 3x = − (2) 7x = (4) 25x = − 9. Which value of y below is the solution to the system shown below? (1) 6y = (3) 4y = − (2) 1y = − (4) 8y = 10. Explain how you can tell that the point ( )5,13 is a solution to the system shown below, without formally

solving the system? 4 7

2 23

y x

x y

= −

+ =

11. Solve the following system of equations below. Show the work that leads to your answer. 2 10

2 5 6

y x

x y

= − −

+ =

2 5 5

3 2 9

x y

x y

+ =

+ = −

4 3 12

2 5

x y

x y

+ =

+ = −2m+ n = −3

8m− 4n = −2

12. What is the solution of the following system of equations?

1) and 2) and 3) and 4) and 13. Solve each system of equations graphically:

y = −x + 4y+ 6 = x

2x + 2y = −2y + 2x −3= 0

14. The functions 2 2 3y x x= − − and 1y x= − are graphed on the grid shown below. Which of the following is the solution set of the equation: 2 2 3 1x x x− − = − ? (1) { }2,1− (3) { }3, 0−

(2) { }3,1− (4) { }1, 4−

y

x

y

x

15. If the quadratic function ( )22 1 8y x= − + + is shown graphed below, then which of the following represents the solutions to:

( )22 1 8 0x− + + =

(1) 0, 3x = (3) 2, 2x = − (2) 4, 8x = − (4) 3,1x = − 16. Sketch the solution set to the system of inequalities shown below.

23

xy x≥

< +

Is the point ( )5,10 a solution to the system? Justify.

y

x

17. Given the system of inequalities shown below, answer the following questions.

2 3

0

y x

y x

≥ +

+ >

(a) Is the point ( )1, 5− in the solution set? Justify without first

graphing. (b) Graph the solution set on the axes provided. 18. Which of the following points is a solution to the set of inequalities shown below? (1) ( )4, 0 (3) ( )3, 2−

(2) ( )0, 2− (4) ( )5, 5−

19. Jody is supplying his food truck for the week. He buys 32 pounds of pork and 50 pounds of chicken for a total of $185. He realizes he did not purchase enough of either and returns to buy 8 more pounds of pork and 20 more pounds of chicken for a total of $65.60. Determine the unit price, in dollars per pound, for the pork and the chicken.

20. Cesar bought 4 magazines and 3 posters for $44. At the same prices, James bought 4 magazines and one poster for $28. What was the cost of each magazine and each poster? [Must be solved algebraically] 21. Lita went to Minewaska Sate Park one day this summer. All of the people at the park were either hiking or bike riding. There were 178 more hikers than bike riders. If there were a total of 676 people at the park, how many were hiking and how many were riding their bikes? 22. For a concert, there were 206 more tickets sold at the door than were sold in advance. The tickets sold at the door cost $10 and the tickets sold in advance cost $6. The total amount of sales for both types of tickets was $6828. How many of each type of ticket was sold?

23.KelandGraysonareeachgoingtoaconcertwithagroupoffriends.Kelbought5ticketsand2parkingpasses,andhespentatmost$80.Graysonbought3ticketsand1parkingpass,andhespentmorethan$30.Whatarethepossiblepricesforticketsandparking?Writeasystemoflinearinequalitiesthatmodelthissituation.Letxequalthepriceofaticketandyequalthepriceofaparkingpass.Kel'spurchase:Grayson'spurchase:Graphthesystemoflinearinequalities. Whichofthefollowingcouldbepossiblepricesfortheticketsandparkingpasses?Selectallthatapply.

24. Dayana is buying Frisbees and Hula Hoops for a family reunion held at Sunken Meadow State Park. Frisbees cost $9 and Hula Hoops cost $5. She plans to spend no more than $45 and buy at least 5 items.

(a) Determinethesystemsofinequalitiesthatrepresentthissituation.

(b) Showthegraphicalrepresentationonthegraphbelow.

(c) ListonecombinationofthenumberofFrisbeesandHulaHoopsDayanacanbuy.

25. Marcus is working at a local pizzeria where he makes $12.50 per hour and is also working at the university bookstore where he makes $9.50 per hour. He must make at least $300 per week to cover his expenses but cannot work more than 30 hours per week in order to attend classes. If p represents the hours he works at the pizzeria and b represents the hours he works at the bookstore, do the following. Write a system of inequalities that models this situation. 26. The Reel Good Cinema is conducting a mathematical study. In its theater, there are 200 seats. Adult tickets cost $12.50 and child tickets cost $6.25. The cinema's goal is to sell at least $1500 worth of tickets for the theater. Write a system of linear inequalities that can be used to find the possible combinations of adult tickets, x, and child tickets, y, that would satisfy the cinema's goal. Graph the solution to this system of inequalities on the set of axes below. Label the solution with an S. Marta claims that selling 30 adult tickets and 80 child tickets will result in meeting the cinema's goal. Explain whether she is correct or incorrect, based on the graph drawn.