Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks. Britney is a costume designer for the local children's theater company. Yesterday, she sewed 5 female costumes and 1 male costume, which used 45 meters of fabric. Today, she sewed 1 male costume, which used a total of 5 meters. How many meters of fabric does each type of costume require? Each female costume requires _____ meters of fabric, and every male costume requires _____ meters.

Question

Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.  Britney is a costume designer for the local children's theater company. Yesterday, she sewed 5 female costumes and 1 male costume, which used 45 meters of fabric. Today, she sewed 1 male costume, which used a total of 5 meters. How many meters of fabric does each type of costume require?  Each female costume requires _____ meters of fabric, and every male costume requires _____ meters.

Bytelearn · Accepted Answer

Set Equations: Let x be the meters of fabric for each female costume and y for each male costume. We get two equations: 5x + y = 45 (from the first day) x + y = 5 (from the second day)Augmented Matrix: Write the system of equations as an augmented matrix: | 5 1 | | x | = | 45 | | 1 1 | | y | = | 5  |Row Operations: To solve the matrix, we'll use row operations to get it into reduced row-echelon form. First, we'll make the element in the first row, first column a 1 by dividing the entire first row by 5. | 1 0.2 | | x | = | 9 | | 1  1  | | y | = | 5 |Subtract Rows: Next, subtract the first row from the second row to make the element in the second row, first column a 0. | 1 0.2 | | x | = | 9  | | 0 0.8 | | y | = |-4 |Divide Rows: Now, divide the second row by 0.8 to make the element in the second row, second column a 1. | 1 0.2 | | x | = | 9   | | 0  1  | | y | = |-5 |

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