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For a certain value of $k,$ the system \begin{align*} 3a + 4b &= 7,\\ 6a + 4b &= k- 4b \end{align*}has infinitely many solutions $(a,b).$ What is $k$?

 Mar 20, 2021
 #1
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3a  +  4b  = 7       multiply through by 2   

 

6a  + 8b =   7    

 

Tthe  second rearranges as

 

6a  + 8b =  k

 

The  system will have infinite solutions  when the  two equations are  exactly the same

 

So...k = 7

 

cool cool cool

 Mar 20, 2021

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