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?
+2666 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 \(\color{brown}\boxed{m = 0}\) and \(\color{brown}\boxed{k = 2}\)
