MHB Using linear systems to solve problems (4)

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Sabrina's earnings from two part-time jobs can be modeled using simultaneous equations. She works a total of 23 hours, earning $9 per hour at her weekday job and $12 per hour at her weekend job, leading to the equations x + y = 23 and 9x + 12y = 231. Solving these equations will yield the number of hours she worked at each job. This approach effectively utilizes linear systems to determine her work hours. The solution will provide clarity on her time distribution between the two jobs.
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Sabrina has two part time jobs delivering flyers. She earns \$9/h at her weekday job and \$12/h at her weekend job. Last week s he worked 23h and earned a total of \$231. How many hours did she work at each job?
 
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bkan21 said:
Sabrina has two part time jobs delivering flyers. She earns \$9/h at her weekday job and \$12/h at her weekend job. Last week s he worked 23h and earned a total of \$231. How many hours did she work at each job?

Hi bkan21, :)

This information can be fit into a pair of simultaneous equations. Suppose Sabrina works \(x\) hours at the weekday job and \(y\) hours at the weekend job. Then,

\[x+y=23\mbox{ and }9x+12y=231\]

Now solve the above two simultaneous equations and find \(x\) and \(y\).

Kind Regards,
Sudharaka.
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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