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Write a system of equations to describe the situation below, solve using an augmented matrix

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Anonymous
0

A TV station executive is planning the new lineup for next season's shows. On Monday nights, there will be 1 sitcom, for a total of 21 minutes of programming, not counting commercials. On Tuesday nights, he has scheduled 6 sitcoms and 2 dramas, for a total of 228 minutes of non-commercial programming. All sitcoms have the same length and all dramas have the same length. How long is each type of show?

Sangeetha Pulapaka
0

STEP 1: Recall what is a system of equations

https://www.purplemath.com/modules/systlin1.html

Before you can solve, you must write a system of equations. Let x = the length of a sitcom, and let y = the length of a drama.


x = 21

6x + 2y = 228


STEP 2: Recall what are augmented matrices

https://www.qalaxia.com/viewDiscussion?messageId=5cff2ee8a6c6ea6528e553ff

STEP 3: Recall on how to solve a system of equations using augmented matrix method

https://www.qalaxia.com/viewDiscussion?messageId=5cff3223a6c6ea6528e5540e

Now use augmented matrices to solve the system of equations


Write them in augmented matrix form

The left part is now the identity matrix, so no more row operations need to be performed.The solution is (21, 51).