Solving Systems of Equations

Solving Systems of Equations

Multiple Choice

Solve for x and y.

y = 2/3x - 2

y = -x + 3

• (0,3)

• (0,-3)

• (3,0)

• (-3,0)

Multiple Choice

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total.

Solve the system:

a + c = 21

6a + 4c = 104

• # of adult tickets = 10

  # of child tickets = 11

• # of adult tickets = 12

  # of child tickets = 9

• # of adult tickets = 11

  # of child tickets = 10

• # of adult tickets = 9

  # of child tickets = 12

Multiple Choice

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.

Which system best represents the situation?

• 4x + 7y = 578

  x + y = 3365

• 4x + 7y = 3365

  x + y = 578

• 4y + 7x = 578

  x + y = 3365

• 4y + 7x = 3365

  x + y = 578

Multiple Choice

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• (35, 52)

• (18, 69)

• ( 52, 35)

• (61, 26)

Multiple Choice

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. How many nickels and dimes did Dennis earn?

• 40 nickels, 40 dimes

• 52 nickels, 28 dimes

• 28 nickels, 52 dimes

• 30 nickels, 50 dimes

Multiple Choice

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

• Sugar Cookies $5

  Oatmeal Cookies $3

• Sugar Cookies $4

  Oatmeal Cookies $8

• Sugar Cookies $2

  Oatmeal Cookies $6

• Sugar Cookies $3

  Oatmeal Cookies $6

Multiple Choice

The sum of Mr. Micklow and Ms. Craft's age is 55. The difference is 3.

Solve:

x + y = 55

x - y = 3

• (26, 23)

• (26, 29)

• (29, 26)

• (29, 32)

Multiple Choice

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

• $5

• $10

• $15

• $20

Multiple Choice

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38

  2s + 3c = 52

• 3s + 1c = 38

  3s + 2c = 52

• s + c = 38

  s + c = 52

• 3s + 3c = 38

  1s + 2c = 52

Multiple Choice

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

• 10c + 5d = 14.25

  5c + 10d = 16.50

• 10c + 5d = 16.50

  5c + 10d = 14.25

• c + d = 10

  5c + 10d = 16.50

• c + d = 5

  5c + 10d = 16.50

Multiple Choice

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

• x + y = 1430

  20x + 50y = 49

• x + y = 49

  10x + 5y = 1430

• x + y = 49

  20x + 50y = 1430

• x + y = 49

  x + y = 1430

Multiple Choice

Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents the situation?

• x - y = -10

  x + y = -2

• x = -2

  y = 5

• x + y = -2

  x - y = -10

• x + y = -10

  x - y = -2