For certain values of k and m, the system
3a + 2b = 2
6a + 2b = k + 3a + mb
has infinitely many solutions (a,b). What are k and m?
Rewrite the second equation to 3a+2b−mb=k.
Now, factor out b to get 3a+(2−m)b=k.
For the system of equations to have an infinite number of solutions, the 2 equations must be identical.
This means that 2−m=2, so m=0 and k=2