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Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding CD a month to his collection while Nita is adding 5 CDs a month to her collection. Write and graph a system to find the number of months after which they will have the same number of CDs. Let x represent the number of months and y the number of CDs.

Find a solution to the following system of equations.

Kendra owns a restaurant. She charges $1.50 for 2 eggs and one piece of toast, and $.90 for one egg and one piece of toast. Write and graph a system of equations to determine how much she charges for each egg and each piece of toast. Let x represent the number of eggs and y the number of pieces of toast.

Which graph represents the following system of equations?
y = 3x + 3
y = –x – 3

Solve the following system of equations by graphing.
–4x + 3y = –12
–2x + 3y = –18

What is the solution of the system of equations?
y = 3x + 7
y = x – 9

Use a graphing calculator to find the solution of the system.
y = x +
y = x +

Find the value of b that makes the system of equations have the solution (3, 5).
y = 3x – 4
y = bx + 2

y = 5x – 4
y = 5x – 5

y = x + 4
y – 4 = x

y = 2x – 3
y = –x + 3

Use substitution to solve the following system of equations.
d + e – f = 11
e = f + d + 5
f = 2e – 12

The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46 centimeters, find the dimensions of the rectangle.

The length of a rectangle is 2 cm more than four times the width. If the perimeter of the rectangle is 84 cm, what are its dimensions?

y = 2x + 3
y = 3x + 1

y = 2x – 10
y = 4x – 8

y = x + 6
y = –2x – 3

3y = –x + 2
y = –x + 9

y = 4x + 6
y = 2x

3x + 2y = 7
y = –3x + 11

The sum of two numbers is 82. Their difference is 24. Write a system of equations that describes this situation. Solve by elimination to find the two numbers.

Sharon has some one-dollar bills and some five-dollar bills. She has 14 bills. The value of the bills is $30. Solve a system of equations using elimination to find how many of each kind of bill she has.

6x + 3y = –12
6x + 2y = –4

2x – 2y = –8
x + 2y = –1

3x + y = 11
4x – y = 17

5x + 8y = –29
7x – 2y = –67

3x – 4y = –24
x + y = –1

x + 2y = –6
3x + 8y = –20

–10x – 3y = –18
–7x – 8y = 11

5x = –25 + 5y
10y = 42 + 2x

3x – y = 28
3x + y = 14

3x – 4y = 9
–3x + 2y = 9

A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. Solve by elimination to find the amount of nickels and dimes that are in the jar.

By what number should you multiply the first equation to solve using elimination?
–3x – 2y = 2
–9x + 3y = 24

An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged $32.00. Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates. She was charged $35.25. What is the admission fee? What is the rental fee for a pair of skates?

Mrs. Huang operates a soybean farm. She buys many supplies in bulk. Often the bulk products need to be custom mixed before Mrs. Huang can use them. To apply herbicide to a large field she must mix a solution of 67% herbicide with a solution of 46% herbicide to form 42 liters of a 55% solution. How much of the 67% solution must she use?

You decide to market your own custom computer software. You must invest $3,255 for computer hardware, and spend $2.90 to buy and package each disk. If each program sells for $13.75, how many copies must you sell to break even?

A motorboat can go 8 miles downstream on a river in 20 minutes. It takes 30 minutes for the boat to go upstream the same 8 miles. Find the speed of the current.

Mike and Kim invest $14,000 in equipment to print yearbooks for schools. Each yearbook costs $7 to print and sells for $35. How many yearbooks must they sell before their business breaks even?

At the local ballpark, the team charges $5 for each ticket and expects to make $1,400 in concessions. The team must pay its players $2,000 and pay all other workers $1,600. Each fan gets a free bat that costs the team $3 per bat. How many tickets must be sold to break even?

Write the following inequality in slope-intercept form.

Find a solution of the linear inequality.

An electronics store makes a profit of $72 for every standard CD player sold and $90 for every portable CD player sold. The manager’s target is to make at least $360 a day on sales from standard and portable CD players.

a.	Write an inequality that represents the numbers of both kinds of CD players that can be sold to reach or exceed the sales target. Let s represent the number of standard CD players and p represent the number of portable CD players.
b.	Write three possible solutions to the problem.
c.	Graph the inequality.

A doctor’s office schedules 10-minute and 20-minute appointments. The doctor also makes hospital rounds for four hours each weekday.

a.	Suppose the doctor limits these activities to, at most, 30 hours per week. Write an inequality to represent the number of each type of office visit she may have in a week. Let x represent the number of 10-minute appointments and y the number of 20-minute appointments.
b.	Graph the inequality.
c.	Is (63, 30) a solution of the inequality?

You have $47 to spend at the music store. Each cassette tape costs $5 and each CD costs $10. Write and graph a linear inequality that represents this situation. Let x represent the number of tapes and y the number of CDs.

Graph the following linear inequalities on the same coordinate plane. What figure does the solution to all three inequalities make?

Graph the following equation.

A local citizen wants to fence a rectangular community garden. The length of the garden should be at least 110 ft, and the distance around should be no more than 380 ft.

a.	Write a system of inequalities that models the possible dimensions of the garden.
b.	Graph the system to show all possible solutions.

You have a gift certificate to a book store worth $90. Each paperback books is $9 and each hardcover books is $12. You must spend at least $25 in order to use the gift certificate. Write and graph a system of inequalities to model the number of each kind of books you can buy. Let x = the number of paperback books and y = the number of hardback books.

Ronald is setting up an aquarium in his new office. At one pet store, fish cost $2 each and an aquarium cost $40. At another pet store, fish cost $3 each and an aquarium cost $36. Write and solve a system of equations to represent the cost of x fish and an aquarium at each store. Solve this the system. What does this solution represent? If Ronald wants 5 fish, from which pet store should he buy his aquarium? Explain.

A motorboat can go 16 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go back upstream the same 16 miles.
Let x = the speed of the boat.
Let y = the speed of the current.

a.	Write an equation for the motion of the motorboat downstream.
b.	Write an equation for the motion of the motorboat upstream.
c.	Find the speed of the current.

Niki has 8 coins worth $1.40. Some of the coins are nickels and some are quarters.

a.	Let q = the number of quarters and n = the number of nickels. Write an equation relating the number of quarters and nickels to the total number of coins.
b.	Write an equation relating the value of the quarters and the value of the nickels to the total value of the coins.
c.	How many of each coin does Niki have?

Write the inequality y is less than x plus 4. Explain how to graph the inequality. Then graph the inequality.

Amy’s restaurant has budgeted at most $60 to spend this month on gourmet coffee. All international blends cost $8.50 per package and all house blends cost $6.00 per package. She would like to purchase some international blends and at least 3 packages of the house blends. How can Amy spend $60 on x international blends and y house blends?

a.	Write a system of linear inequalities that describes this situation.
b.	Graph the system.
c.	Give a possible solution and describe what it means.

Tim has $12 to spend at the produce market. He wants to buy some tomatoes at $3 per pound, and some apples at $2 per pound. Tim writes the following linear inequality to determine how many pounds of each item he can buy; . Explain what values of x and y are reasonable.

Without solving, what method would you choose to solve the system: graphing, substitution, or elimination? Explain your reasoning.

Without solving, what method would you choose to solve the system: graphing, substitution, or elimination? Explain your reasoning.

Describe how to determine when elimination should be used to solve a system of equations, and how to determine whether to use addition, subtraction, or multiplication.

Tickets to a local movie were sold at $6.00 for adults and $4.50 for students. There were 240 tickets sold for a total of $1,155.00.

a.	Write a system of equations to model the situation.
b.	Solve the system to find the number of adult tickets sold and the number of student tickets sold.
c.	Explain the method you used to solve the system.

Without graphing, decide whether the system has one solution, no solution, or infinitely many solutions. Explain.