Linear Systems by Matrix

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 using matrices:

x + y = 21

6x + 4y = 104

• (10, 11)

• (12, 9)

• (11, 10)

• (9, 12)

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. Using matrices, what would be your solution as to how many nachos and soda he sold?

• (35, 52)

• (18, 69)

• ( 52, 35)

• (61, 26)

On the first night, the Movie House Theater sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. Find the price of an adult ticket and the price of a child ticket using matrices on your calculator.

• Adult $13

  Child $5

• Adult $10

  Child $6

• Adult $8

  Child $16

• Adult $12

  Child $13

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

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• a

• b

• c

• d

• a

• b

• c

• d

Solve the linear systems together by using the values of b for two separate systems, then reducing an appropriate augmented matrix to reduced row echelon form. Write your answer as (x1, x2), (x1, x2) form.

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Solve the system by inverting the coefficient matrix and using (A^-1)(x)=b. Enter your answer as (x1, x2) format.

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A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60