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avatar+17 

For a certain value of the system: 

\(3a+4b = 7,\)

\(6a+4b = k-4b\)

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

 May 14, 2022
 #1
avatar+2432 
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Simplify the second equation to: \(6a+8 b=k\).

 

For a system of equations to have infinite solutions, the two equations must be a multiple of each other. 

 

Note that the second equation is twice the first equation. 

 

Can you take it from here?

 May 14, 2022
 #2
avatar+75 
+1

k=14

 

Explanation:

First, put the like terms on the same side. 6a+4b=k-4b turns into 6a+8b=k

 

Then you can multiply the top equation by 2 to get 6a+8b=14

 

Now, you have the system of linear equations, 

 

{6a+8b=14,

{6a+8b=k

 

Therefore, k must be equal to 14.

 May 14, 2022

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