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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?

 Apr 6, 2022
 #1
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We can write

 

3a + 4b  = 7

9a + 12b = k

 

We have infinite solutions when one equation is a multiple of the other.....so.....

 

Note that  multiplying the first equation through by 3 we get.....  

 

3 (3a + 4b)  =  3 * 7

 

9a + 12b  =  21  =  k

 

 

cool cool cool

 Apr 6, 2022
edited by CPhill  Apr 6, 2022

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