Systems of Linear Equations and Matrices

Solve the system of equations using Gaussian Elimination.

25x + 60y + 80z = 510

40x + 20y + 15z = 325

60x + 90y + 100z = 840

• (6, 2, 3)

• (3, 2, 6)

• (6, 3, 2)

• (3, 6, 2)

Write the augmented matrix for the system of linear equations.

2w – 3x + 4z = –12

–3w + 6y – 9z = 7

–x + 4y – 5z = 2

w + 6x + 4y = –9

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Find the inverse of 

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Solve the system of equations: 

• ( -1, 6, 1)

• ( 1, 6, -1)

• None of these

• ( -6, -1, 1)

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $68 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

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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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• a

• b

• c

• d

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

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