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For a certain value of k, the system

 

3a + 4b = 7,

6a + 4b = k - 3a - 8b

 

has infinitely many solutions (a,b). What is k?

 Dec 19, 2021
 #1
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The first equation is:  3a + 4b  =  7

 

The second equation is:    6a + 4b  =  k - 3a - 8b

which becomes:              9a + 12b  =  k

 

Multiplying the first equation by 3:  9a + 12b  =  21

 

For these to have infinitely many solutions, these must be two forms for the same equation; so  k = 21

 Dec 19, 2021

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