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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?

 Feb 6, 2022
 #1
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First equation:  3a + 4b  =  7

Simplifying the second equation:  6a + 4b  =  k - 3a - 8b

                                                    9a + 12b  =  k

 

To have infinitely many solutions, get the coefficients of a and b to be the same:

   

    first equation:            3a + 4b  =  7     --->   x3   --->     9a + 12b  =  21

    second equation:                                                          9a + 12 b  =  k  

 

There will be infinitely many solutions when  k = 21.

 

(There will be none if  k isn't 21.)

 Feb 6, 2022

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