For a certain value of the system:

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

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

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

ChocoSwirl May 14, 2022

#1**0 **

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?

BuilderBoi May 14, 2022

#2**+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.

idontknowhowtodivide May 14, 2022