how do you use an inverse matrix to solve the linear system 5x+y=6 9x=2y=30

Might be a different Anonymous Melody.  That's the problem with Anonymous - he/she is a multi-headed beast!

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There is an error in your question.

You have 2 equal signs in your second equation.  

If we assume your second equation is 5x + 2y = 30 (because there are + and = signs on the same key on many keyboards) then:

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Hi Alan, you missed two negative signs in your definition of Inv(M).

No, I don't think so:

Or did you mean in the general expression with the a, b, c and d?  Here you need to look closely at the top right and bottom left terms to see the minus signs. At a glance they can look like a continuation of the division line!  This is a facet of the software I used to generate the expression - I've missed them myself in the past! 

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You know anon - picking up possible errors is fine but it is important to throw in a thank you as well.

Alan did a lot of work on your behalf!

Hi Alan,

Even if it is a different anon they can still acknowledge the work that you have done.

Hi Melody,

Because the message started with the words "Hi Alan,..." I took it as a friendly pointer to a possible error (let's face it, I make enough mistakes!).

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We all make mistakes, you certainly do not make any more than any one else.  :)))