Can anyone help here? I keep trying, but I can't get the right answer.

For a certain value of k, the system

3a + 4b = 7

6a + 4b = k + 3a

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

Simplify 6a+4b=k+3a to get 3a+4b=k.

If:

3a+4b=k

and

3a+4b=7

then the two equations must be equal, so k=7.